The Long Count: Astronomical Precision
FIXING THE DAY THE WORLD BEGAN
Following the development of the sacred and secular calendars in Izapa in the fourteenth century B.C., their diffusion continued throughout the length and breadth of Mesoamerica during the following two millennia, having most likely reached the Maya highlands of what is now western Honduras by about the fifth century A.D. Although many different peoples of Mesoamerica had by then come under the influence of the two time-counts, including the Zapotecs, Mixtecs, Teotihuacanos, and Maya, it is probably safe to say that the diffusion process itself can largely be attributed to the migrations, military exploits, and "missionary" activities of the 0lmecs. Certainly, central to their role as the "Mother Culture" of Mesoamerican civilization was their preoccupation with time, the elaborate set of religious rituals which they had created to celebrate it, and the distinctive numerical and glyphic systems which they had devised to record it. And common to all of the cultures which had come under the calendars' influence had been the rise of ceremonial centers and urban places whose very locations had been fixed by marking in space certain key points in time, such as the solstices and the sunset on August 13. As yet, of course, the calendars' impact on the Nahua peoples had not even begun, for their arrival in the Valley of Mexico was still at least a century away.
So, too, had the peoples and cultures of western Mexico remained innocent of the Olmecs and their advances (Adams, 1991, 113), largely, it would seem, owing to the relative isolation of the region caused by its topographic ruggedness. (Kent Flannery's argument  that the region was ignored because the Olmecs tended to deal only with societies of equal sophistication is scarcely credible, because the Olmec were everywhere the dominant cultural and commercial actors at the time; hence, they would have had no one with whom to interact if that had been the case.) Although some traces of contacts with the plateau are to be found at El Opeño as early as 1300 B.C., it was not until well into the Christian era that Mesoamerican high cultures began to penetrate the mountain fastnesses of the Mexican west (Adams, 1991, 113).
As a result, the coastal regions of Colima, Jalisco, and Nayarit continued to enjoy closer cultural bonds with South America through this period than with the Mesoamerican heartland. In Middle Formative times (800-500 B.C.), the lower reaches of the Balsas River (in what is now Michoacán state) were the site of the so-called Infiernillo phase burials, once more associated with a distinctive type of pottery. By 250 B.C. a new funerary custom, the so-called shaft tomb, was spreading rapidly through the alluvial lowlands of Colima, Jalisco, and Nayarit and subsequently into the interior up along the Santiago corridor. A cultural trait whose origins can be traced back to Peru, Ecuador, and western Colombia, it ultimately penetrated as far inland as the Lake Chapala region. The northern Michoacán site of Chupícuaro, now covered by an irrigation reservoir, appears to have been the main contact point between the cultures of the highlands and the west during the centuries bracketing the beginning of the Christian era (Adams, 1991, 121).
About the same time that Chupícuaro was reaching its peak as an interactive border post between the two culture worlds, another advance in intellectual sophistication was unfolding in the Mesoamerican heartland. It was perhaps inevitable that, with the passage of time, new and more exacting demands would be made of the calendars, giving rise to innovations in their use that were totally unforeseen at the time of their creation. For example, even though the 365-day secular calendar had attained an improved margin of accuracy over the 260-day sacred almanac, it still missed calibrating the true length of the solar year by about a quarter of a day per year. But for a people who could not comprehend the concept of fractions, there was no obvious way that this matter could ever be reconciled -- at least in other than the manner they chose, which was to ignore it.
Nevertheless, because the two calendars ran concurrently, certain realities of their operation must gradually have became apparent to the priests who were responsible for using them. For one thing, they would have realized that the lowest common denominator of the two time counts amounted to 18,980 days. This is because the sacred almanac of 260 days would require 73 rounds to bring it back into phase with the secular calendar of 365 days, which during the same period would have completed 52 rounds. In other words, 260 x 73 = 18,980, whereas 365 x 52 yields the same result. Thus, all Mesoamerican societies came to believe that "history repeats itself" every 52 years -- for if, for example, the beginning day of the sacred almanac, 1 Imix, had fallen on the beginning day of the secular calendar, 0 Pop, in a given year, then it would take 52 years before the same two day-names and -numbers would again coincide.
For most of the peoples to whom the Olmecs bequeathed the calendars, no further sophistication seemed necessary. After all, the average longevity of a typical person in those days was probably not much more than 30 years, so it would have been the rare individual indeed who would have lived to see the same day-names and -numbers recur within his or her lifetime. In fact, in many of the cultures the 52-year period was itself equated with a "lifetime," whereas a double-period of 104 years was referred to as the lifetime of "a very old person." As a result, in most of the cultures, important events, such as the births and deaths and accessions to power of key members of the society, were seldom specified more closely than to the 52-year period in which they occurred. Thus, when we find glyphs telling of a personage by the name of "8 Deer," we know that the given individual was born on a day with that number and name, but we can't pinpoint the calendar year in which the event occurred unless we know the specific 52-year cycle during which it took place. This custom of citing dates only in terms of a given 52-year cycle has been called the "Short Count," especially by researchers working with the Maya.
However, the association of the Short Count with the Maya is only accurate of their final period of decadence and decline, for through most of their brief but illustrious history, the Maya employed a different, very precise calendrical notation which has come to be known as the Long Count. To credit them with the development of the Long Count would be to misread the facts of the calendars' evolution; this, too, seems clearly to have been an Olmec creation -- and indeed, both a brilliant and precocious one at that.
We can only guess at what prompted its development. Perhaps it was simply the dissatisfaction with a time-reckoning system that had so little concern for history that it couldn't define the great events of a society closer than to a given 52-year period. Or perhaps it was an attempt to "squeeze" more precision out of the two time-counts, neither of which recorded the celestial cycles with convincing accuracy. Or was it intended to facilitate more sophisticated computations, such as those involved in the prediction of eclipses? Or perhaps it was just some priest's means of "guesstimating" when the world had begun? After all, these kinds of questions have likewise prompted the various dabblings which have occurred from time to time in Western civilization, not alone with our own present Gregorian calendrical system but with the previous Julian system as well.
The first clue as to when the Long Count was devised is found in the coefficient established by the Goodman-Martínez-Thompson correlation. Each of these researchers realized that the Mayan calendrical glyphs always had reference to a day called 4 Ahau 8 Cumku as the beginning date of their count. This means that the Maya believed that the present epoch of the world began on a day numbered 4 which coincided with the last name (Ahau) of a 20-day "bundle" of the sacred almanac and which coincided with a day numbered 8 which fell in the last 20-day "month" (Cumku) of the secular calendar. (All Mesoamerican cultures believed that the world had existed in four earlier epochs, each of which had been terminated by a different kind of cataclysm. For example, the Aztecs believed that the first world, or "sun," began on a day named "4 Water," and that it came to an end on a day with a similar name as a result of great floods. The second "sun" began on "4 Ocelot," and was terminated on a day of the same name when tigers devoured the world. The third "sun" was called "4 Rain" and was destroyed by a deluge of fire and brimstone on another day of that name. The fourth "sun" was called "4 Wind" and was ultimately ended by a tempest on a day of that name. Our present world, "4 Movement," began on a day with that name and will end with great earthquakes on some occasion when the calendar reaches that day-name again [Krickeberg, 1980, 231.)
Thus, if we were to restate the Maya description of the beginning of the present world in terms of our own calendar, it would be like saying that it had begun on a day numbered 4 which was a Saturday about the middle of December. What had happened during the earlier three days, or in the week before Saturday, or in the course of all the months before December, didn't seem to bother the Maya. Whereas someone growing up in the Western cultural tradition would probably have believed that "beginnings should be beginnings" and that it would "make more sense" if the world had begun on a day like Sunday which fell on the first of January, this was surely not the thought process of the Maya.
In fact, it is just because the Maya date for the world's creation is so "strange" that most researchers recognize it as a hypothetical reconstruction made well after the calendar was in everyday use. Indeed, it was a case not unlike the Romans tracing the mythological founding of their city to Romulus and Remus in 759 B.C., or Bishop Usher fixing the creation of the earth at 10 A.M. on October 23, 4004 B.C. by using the Bible as his authority. But what remained to be established was the correspondence between the Maya date of 4 Ahau 8 Cumku and a date in our own calendar, and this is what Goodman, Martínez, and Thompson each independently set out to do. (Of course, well over a score of other researchers have sought to do the same thing, but none of these other correlations have proven to be as convincing as that of these three scholars.)
Joseph Goodman was a newspaper editor in Virginia City, Nevada, back at the turn of the century. A friend of Mark Twain, he was also a " puzzle buff," and in his readings he came across mention of the strange Maya date and the question as to what it might correlate with in our own calendar. In 1905 he published a short article in which he put forth the results of his computations, namely, that the Maya date could be equated with August 11, 3114 B.C.
Of course, there were no bona fide archaeologists in Goodman's day, so little or no professional notice was taken of his deductions. A couple of decades went by before a Mexican astronomer independently tried his hand at the problem. In 1926, Juan Martínez Hernández came up with a date which placed the beginning of the Maya calendar one day later, on August 12, 3114 B.C. This time, however, the result was not ignored, having been advanced by a professionally trained academic. Of course, that did not necessarily make it correct, so British archaeologist John Eric Sydney Thompson put his mind to the problem and a year later, in 1927, published his findings. Based on his examination of Maya eclipse tables, the correlation of 4 Ahau 8 Cumku should be one day later still, he said, placing it at August 13, 3114 B.C. (It is because all three of these researchers came to virtually the same solution that this correlation has come to be called by all of their names.)
As it turned out, if Thompson had left well enough alone, a subsequent generation of archaeologists, astronomers, and other aficionados of prehistory would have found life a lot easier. But, in 1935, Thompson had "second thoughts," deciding not only that Goodman had been correct in the first place but also that the Maya really weren't astronomers after all, but only "astrologers." This meant that the correct date was indeed August 11, 3114 B.C., and that later researchers would be ill advised to look for astronomical meanings behind Maya dates, because if they found them, they could only be "coincidences." The dean of Mesoamerican archaeologists having spoken, the matter was finally settled -- or so they thought.
When I published my hypothesis of the origin of the 260-day Mesoamerican sacred calendar in Science in September 1973, one of the first responses I received was from Sir John Eric Sydney Thompson, recently knighted by Queen Elizabeth II for his substantial professional contributions to the discipline of archaeology. Short and terse, Thompson's note chided me for "overlooking" his book from 1950 in which he claimed to have effectively disposed of any astronomical arguments for the calendar's creation, even going so far as to cite the specific pages I had missed. I dutifully reread the passages he alluded to, and after considerable thought and some trepidation -- I had never before written to a knight of the British Empire -- I wrote, "I had read the pages you cited, but I thought you were wrong then and I still think you are wrong." Needless to say, that was the end of our correspondence -- but certainly not of the controversy which surrounds the so-called Maya calendar. (Indeed, as the reader will already have discovered, this is largely what the present volume is all about.)
Thompson's understanding of how the 260-day almanac arose came down to one of two possibilities: Either it represented a permutation of the numbers 13 and 20, both of which had a special significance to the Maya, or it represented an approximation of the human gestation period. In any case, he argued that it had nothing to do with astronomy. When it had been pointed out to him by Merrill in 1945 that the zenithal passage of the sun over Copán -- the major Maya astronomical center in the mountains of western Honduras, located at precisely the same latitude as Izapa -- occurred on August 13, the day that his own correlation originally indicated the Maya had believed was the "beginning of the world," he had dismissed it as a "coincidence." Of course, when Thompson "revised" his date for the origin of the Long Count to August 11, that automatically put all subsequent attempts by astronomers to reconcile the Maya calendar with our own off by two days -- making the argument of "coincidence" seem all the more credible. On the other hand, neither Thompson nor any of his disciples has ever explained when the permutation of 13 and 20 actually was carried out to put the Long Count in motion, or whose gestation period was so significant as to base the starting point of an entire calendrical system on it. Indeed, while birth makes it perfectly clear when a gestation period has ended, what recorded act specifically defines when it began? Or, for that matter, how do we know that it actually took 260 days to complete? If modern science is at pains to define the moment of conception, how in the world could the early Mesoamericans have decided that the length of the gestation period was precisely 260 days?
Ironically, in the same vein, some writers on the subject of the Mesoamerican calendar have taken me to task because my explanation of the 260-day almanac's origin is 2 days at variance with Thompson's revised formula. Had it ever occurred to them that Thompson might have been right the first time, perhaps they wouldn't persist in such specious arguments.
It seems extremely unlikely that the "New World Hipparchus" who was responsible for the development of the 260-day sacred almanac and the 365-day secular calendar had any other intent in mind than to devise a means of recording time or, even more specifically, of predicting the advent of the rainy season. Certainly, there could be no notion whatsoever that either calendar -- especially one that he himself had been instrumental in developing -- should attempt to define "when the world began"; after all, he himself had been around before the calendar was, and the world, in turn, was obviously a lot older than he. Such an idea would probably have been as preposterous to him as the notion of fractions! Indeed, perhaps he would have been hard-pressed to think in any longer spans of time than from one rainy season to another, because that, after all, was what the calendar was all about -- at least to him.
Any notions of "history" or ideas of time as an ongoing continuum must have been the product of a mind or minds that could have contemplated the whole question from the vantage point of a considerable hindsight. After all, as the initial Olmec priest himself recognized, a day has not really existed until it is over. By the same token, a person's lifetime, or a 52-year cycle, has not really existed until it has been completed. Only after several generations have passed is the notion of "history" even possible. And when it becomes desirable or useful to characterize the span of history, it is necessary to do so in units of time and in a context that has meaning to the society for which the history is being devised. Thus, Christians calibrate history according to the birth of Christ, Muslims according to the Hegira of Muhammad, etc.; and no doubt because we are accustomed to using a decimal system, we find it convenient to speak in terms of "decades" and "centuries" -- though on a human scale such measures as the latter are rather meaningless.
In a culture which employed a vigesimal system and for which the number 13 had a special, if not magical, importance, it is not surprising that the most meaningful units would have been some multiples of these values. The most basic unit was the day, known as a kin, or "sun," in Mayan. The second-order unit was a "bundle" of 20 days, which we have called a uinal, or literally a "moon." The third-order unit we have called a tun, and it represents the one deviation from the vigesimal system which the Maya permitted themselves. Composed of 18 "bundles" of 20 days, rather than the full complement of 20 "bundles," it was in recognition of the fact that 360 days is a much closer approximation to a length of a year than 400 days was. (For all measures other than time, however, the strict vigesimal system was employed.) The fourth-order unit consisted of a "bundle" of 20 tuns, or what we have called a katun. Because each tun was five days shorter than an actual year, each katun equated to a time span of 19 years and 260 days, for a total of 7200 days in all. Because these were the most "human-scaled" units of the Maya calendar, Thompson contended that katuns were the most important "building blocks" of their timekeeping system. (More about this later.)
The fifth-order unit is the so-called baktun, which consists of a "bundle" of 20 katuns, or a total of 144,000 days (i.e., 20 x 7200). Equated to a measure which is somewhat more meaningful to us, a baktun represents a span of time 394 years and 95 days in length. Yet another interval of time as the Maya conceived it was what we call a "grand cycle," composed of 13 baktuns, which can likewise be translated as "a world." If the present world began on August 13, 3114 B.C., then it is due to end on December 23, A.D. 2012, according to the Maya, because that is when the 13th baktun will be complete.
But where, and by whom, was this "master plan" of Maya world history devised? Again, one must look to the internal structure of the so-called Maya calendar to see what clues it affords us. If katuns were the most significant "building blocks" in the Maya time-count, as Thompson has argued they were, then I would suggest that the manner in which to begin is to find out how many times a katun has ended on 8 Cumku. This was the date in the secular calendar, it will be remembered, that our unknown history-minded priest had decided that the world had begun, most likely because he was looking for a time to assign to the zenithal sun's passage. (Whether or not he knew where the zenithal sun had passed overhead on that special day, he was certainly aware that that passage had been the mechanism for starting the calendar, as we shall clarify later.)
By designing a computer program which used as its beginning date the correlation between Maya and Gregorian calendars worked out by Goodman -- namely, that 13 Ahau 8 Xul equaled November 4, A.D. 1539 --1 proceeded to run the program backward, having instructed the computer to indicate each time that a katun ended on 8 Cumku. The first time that the computer stopped was on 8 Ahau 8 Cumku, which equated to the date of September 23, A.D. 1204. This, of course, was well, after the Classic Period of the Maya had come to a close and their civilization was in decline, so this result could quickly be discarded. The next time the computer stopped was on 11 Ahau 8 Cumku, which equated to a date of September 18, 236 B.C. (This seemed like a feasible date, but I was not prepared to make any judgment until all the evidence was in. Naturally, because there was a full 1440-year interval between the first computer result and the second, it was already apparent that if the same interval occurred before the next result was in --which was more than likely -- then the final result would be far too old.) Sure enough, the only other time that a katun had ended on 8 Cumku was on September 13, 1675 B.C., when 1 Ahau corresponded with that date. I therefore was led to conclude that whoever had projected the time-count back into history had done so in the year 236 B.C., because this was the only time frame that would have been consistent with what we know of Maya history. This meant that the day on which this projection had been made was identified in the Long Count -- which was now being used to record dates for the first time -- as 126.96.36.199.0. In other words, the creator-priest of these newly meshed time-counts had decided that seven baktuns and six katuns had elapsed since the theoretical "beginning of the world."
It should be noted that a Maya Long Count inscription must contain a minimum of nine terms to define it. First, there are the five numerals describing the number of baktuns, katuns, tuns, uinals, and kins, respectively, which have elapsed since "the beginning of time." These are followed by the number and day-name of the date in the sacred almanac and then by the number and day-name in the secular calendar. As a result, the date that was recorded was absolutely unique, Even so, at some later time, other glyphs were added to the inscription to make it astronomically yet more precise, as for example, by enumerating how many days had elapsed since the last new moon.
The result which had been produced by my computer program was entirely consistent with what we knew of Maya inscriptions, because none had ever been found which predated the seventh baktun -- a period of time that ran from 353 B.C. to A.D. 41. On the other hand, what the 236 B.C. date did show rather conclusively was that the so-called Maya Long Count was not a product of the Maya at all, but rather the creation of their predecessors, the Olmecs, for civilization (in the sense of ceremonial centers and monumental structures) had not even reached the Maya at this juncture in their history.
Unknown to me at the time I had launched my computer investigation of the Maya calendar was the fact that in 1930 a mathematician by the name of John Teeple had come to exactly the same conclusion, but had done so by approaching the question of the Long Count's origin from quite another direction than I had taken. Having recognized how the recurrence of the 73 cycles of the 260-day sacred almanac coincided with the 52 years of the secular calendar, Teeple had suggested that what the Maya had done was to use a multiple of 73 katuns to arrive at their hypothetical "beginning of time." Of course, he was unaware that the designer of the Long Count was impelled to establish an August 13 starting date for the count, regardless of how many katuns were thought to have intervened. As a result, Teeple's formula was to employ two cycles of 73 katuns, or 146 katuns in all, to reach the point in time when he believed the Maya priests had chosen to initiate the Long Count. One hundred forty-six katuns, of course, can be broken down into seven baktuns plus six katuns; thus, the Maya date on which Teeple concluded the Long Count had been commenced was 188.8.131.52.0 (Teeple, 1930).
When I carried out my computer analysis of the Maya calendar, I was also unaware that Thompson had likewise taken note of Teeple's computation. However, while lauding him as "a brilliant mathematician," he had dismissed his result as unlikely and unconvincing, thereby effectively consigning Teeple's conclusion to the trash-heap of oblivion -- at least until I inadvertently reinforced it with my own finding. Ironically, the realization that I had been "anticipated" by Teeple was reassuring to me, because even though we had approached the problem from very different vantage points, we had arrived at the same conclusion. On the other hand, even though I now found myself in the company of "a brilliant mathematician," I was even further at odds with the dean of Maya archaeologists!
MATHEMATICS WITHOUT TEARS
Perhaps the initial motive for devising the Long Count was an attempt to give the Olmecs some perspective of history, and in that, it was singularly successful. Time could now be appreciated as a continuum, and its expanse was infinite. When the Olmecs spoke of the "beginning of the world" or "the beginning of time," it may have been only the "present world" they had in mind. On the other hand, there is good reason to believe that they conceived the current "grand cycle" of 13 baktuns in which they existed as but one more reincarnation of worlds that have existed in the past and but one more step on the way toward future worlds. In any event, common to all later Mesoamerican cultures was the notion that four previous worlds had already come and gone.
But while there was something philosophically reassuring about the view of time which the Long Count afforded them, the Olmecs also found that it was an eminently practical device as well. Now they had a means of defining every day that passed as being absolutely unique -- at least within a time span of one "grand cycle," or 5125 years. And the position of every day within that round of 13 baktuns, or 1,872,000 days, was numbered consecutively from "the beginning." The imprecision of the Short Count, or defining a day within a given 52-year period, was gone. Human life spans lost their meaning when compared to the "life spans" of the sun, moon, and stars, and of the celestial rhythms which governed their movements. The Long Count had opened a whole new vista, not only in history but also in mathematics.
The principles of zero and place notation had already been worked out by our "New World Hipparchus" when the secular calendar had been set in motion; the Long Count now just put those principles into use as never before. Many of the secrets of the heavens remained to be deciphered, and certainly one of the most pressing -- primarily because it was so frightening -- was the seemingly random disappearance of the sun or moon. Was there a cycle between such happenings, they asked? Was there a way that they could keep careful enough records so that they would eventually know when such a happening was going to take place? For that matter, what really was the cycle between two full moons, or two new moons? And surely one of the most problematical of celestial bodies -- the third-brightest object in the heavens after the sun and moon -- had to be Venus. Its importance could not be doubted, but its erratic behavior -- first as morning star, then disappearing, next as evening star, and then disappearing again -- seemed to defy explanation. After all, in a culture where fractions did not exist, the counts could become long and involved before any celestial cycle such as that of the moon or Venus would emerge with a number of whole days. At least, when all the days were reduced to numbers, counting them was far simpler, especially the longer it took to define such a cycle.
A case in point was the determination of a lunation -- that is, the time between one full moon and another, which modern atomic clocks record as just less than 29.5306 days. The closest approximation the Maya ever made to this interval was by counting full moons for 12 tuns and 80 kins, by which time 149 lunations had taken place in exactly 4400 days. At this point, they were only about 0.0004 off the value we use today. Thus, even though they were handicapped by their inability to conceive of fractions, the Maya, through long and patient counting, were able to achieve a level of precision in their astronomical studies which few other early peoples in the world ever matched.
It is interesting that amid the renaissance of European science the same idea of assigning each and every day its own distinctive number -- also to facilitate the calculation of astronomical intervals -- surfaced once again. This time it was a French-born Italian by the name of Joseph Justus Scaliger who devised the count and the year was 1582. A true Renaissance man, Joseph Scaliger was the son of a classical philologist and medical doctor who had lived and worked in France and made his primary reputation as a poetry critic. Joseph himself became a professor at the University of Leiden in the Netherlands in 1593 and made significant contributions to such fields as numismatics, epigraphy, and literary analysis, in addition to chronology.
Scaliger, like his Mesoamerican predecessor eighteen centuries earlier, was a product of his own culture and was constrained not only by a starting date that was fixed by the calendar with which he was familiar but also by one that had a special astronomical significance. Indeed, a further constraint under which he operated, which most probably had not been a concern of his Mesoamerican counterpart, was his own appreciation of history. Scaliger lived at a time when the true antiquity of the Egyptian and Near Eastern civilizations was just beginning to be appreciated, so his time-count would have to accommodate events that may have happened at least as far back as 4000 B.C. In other words, if Scaliger did not choose his starting date carefully enough, computations involving very ancient observations from places like Egypt would necessarily involve negative numbers and this would have served more to complicate his case rather than to expedite it.
Not too surprisingly, Joseph Scaliger chose January 1 as the beginning day of his count, but of course it had to be a very special January 1 that had occurred before 4000 B.C. By searching the astronomical records and making his own computations, he discovered that in the year 4713 B.C., the 28-year solar cycle, the 19-year lunar cycle, and the 15-year indiction cycle would all have coincided. (The latter, interestingly enough, was a concept widely used in medieval chronological studies but had nothing to do with astronomy. Rather, it was related to the tax reassessment system used in the Roman Empire, and probably had been originally adopted from Egypt.) Inasmuch as the least common multiple of the three cycles was 7980 years (i.e., 28 x 19 x 15), any day could be identified within that span of time with absolute specificity. Both the 7980-year period and the day-count within it he named for his father, Julius Caesar Scaliger, and thereby added two new concepts to the tool kit of Western science: the Julian Period and the Julian Day number. Needless to say, although the former is now regarded as "quaint" and anachronistic, we continue to use it because there has been no compelling reason to start counting over from some other date. In other words, January 1, 4713 B.C., continues to serve the Western world as well today as the date August 13, 3114 B.C., appears to have served the Mesoamerican world for well over a millennium.
Before we leave this matter of the Long Count and its belated European counterpart, let us pause a moment to consider the relationship between them. This, after all, is what the correlation of the two calendrical systems is all about. To establish the Julian Day number of the date on which the "New World Hipparchus" began his count of the 260-day sacred almanac, we first must subtract the number of years between the time that the Julian Period began and when the Olmec time-count was set in motion. Keep in mind that the term "Before Christ," or "B.C.," is a historical denomination rather than an astronomical one, because historians recognize no "year zero," whereas astronomers do. Thus, 4713 B.C. in historical parlance is the equivalent of -4712 in astronomical usage. As long as the two dates in question both lie on the same side of Christ's "birth," there is no problem, but when one of the dates is "B.C." and the other is "A.D.," it should be remembered to subtract one year between them. One other thing to remember is that when Scaliger set up his Julian Day numbers in 1582, he was using the so-called Julian calendar (named not for his father but for Julius Caesar). By that time, however, the Julian calendar had gotten so far out of phase with the realities of the solar year that Pope Gregory XIII decreed the adoption of a new and more accurate calendar in October of that very year. This is the so-called Gregorian calendar which the Western world uses today.
Returning to our computation, we find that there were 1599 years which elapsed between 4713 B.C. and 3114 B.C., for a rounded total of 584,035 days according to the Julian calendar (which used 365.25 days as the length of the solar year). Of course, this represented the number of days between January 1 in both years, so we have to add a further 225 days to reach August 13. This means, then, that a total of 584,260 days had elapsed between the two dates using the formula supplied by the Julian calendar.
However, the reason that the Julian calendar had finally to be abandoned was that it was using a value for the length of the solar year which was 0.0078 days too long, because the actual length of the solar year (as determined by modem science) is not 365.25 days but 365.2422 days. As a result, the Julian calendar gained a day every 128 years, so that by the year 1582, when Pope Gregory finally tackled the problem of calendar reform, the vernal equinox had slipped from March 21 to March 11. (Even though the ecclesiastical council which met at Nicaea in 325 had decided that the vernal equinox should always fall on March 21 -- as it did in the period from the year 200 to 325 -- in order to expedite the fixing of the date of Easter, they had done nothing to rectify the calendar to insure that this would happen.)
To understand how a date in the Gregorian calendar would vary from one in the Julian calendar, it is necessary to subtract 325 from any year following the year 325, or to add 200 to any year preceding the year 200. Thus, in 1582 the number of years which had elapsed between the time that the Julian calendar was in phase with reality -- as measured by the vernal equinox occurring on March 21 -- and the time that the Gregorian calendar supplanted it was 1257, namely 1582 - 325 = 1257. Dividing this in turn by 128 reveals that the slippage of the Julian calendar within that time period was 9.8 (or 10) days.
By the same token, if we wished to calculate how great the disparity would have been between the Julian calendar and the Gregorian calendar in recording a date such as 3114 B.C., we add 200 to 3114 to obtain the number of years which elapsed between them (200 + 3114 = 3314) and then divide this by 128. The result in this case is 25 days, which must be added to the total of 584,260 which had elapsed between the beginning of the Julian Period and the theoretical date of the Maya's "beginning of time." Thus, the Julian Day number for August 13, 3114 B.C. is 584,285 -- the value used by the (initial) Goodman-Martínez-Thompson correlation to calibrate the Maya calendar with the Gregorian.
THE GEOGRAPHIC DISTRIBUTION OF EARLY LONG COUNT INSCRIPTIONS
In establishing the geographic birthplace of the Long Count, the spatial distribution of the earliest known inscriptions may be of some assistance. Admittedly, the sample is small, for there are only eight known inscriptions which date from the first baktun of the Long Count's existence.
The oldest of these is Stela 2 found at Chiapa de Corzo, in the heart of Mexico's southernmost state, Chiapas. Although it had been broken at the top such that the baktun numeral is missing, Gareth Lowe, who discovered the monument in 1962, transcribes its date (184.108.40.206.13 6 Acatl) as December 10, 36 B.C. In doing so, he followed a line of reasoning which was first employed when a similarly broken stela had been unearthed in the Gulf coastal plain more than 20 years earlier. In the process, what had been the oldest known Long Count inscription was "bumped" into second place.
The second oldest Long Count inscription which has been found up until the present time occurs on a stela from Tres Zapotes, near the northern edge of the Tuxtla Mountains in the state of Veracruz. Known as Stela C ever since it was uncovered by Matthew Stirling during his excavation there in 1939, it early became a bone of contention between "Mayanistas" and "Olmequistas" (Ochoa and Lee, 1983, 181). The fact that its baktun number was missing, the stela having been broken at that point, only fueled a controversy that had long been brewing. If the missing baktun numeral had been a seven, Stela C would have been the oldest known example of a monument bearing a Maya Long Count date. But because its geography was all wrong, having been discovered in a classic Olmec area, "Mayanistas" such as Thompson and Morley argued that either the baktun numeral had been an 8, meaning that the Long Count had diffused into the Olmec area long after the Maya had devised it, or it was a "copy" of the Maya Long Count date which simply used a different (and by implication, later) starting date. Protagonists of the Olmec school, on the other hand, argued that the only calendrical inscriptions found outside of the Maya area until that time had all been of baktun 7 origin, so why should it be supposed that this was any different? In any case, by sheer good fortune, the missing piece of the stela was found in 1969 and the baktun value was indeed a seven! Its complete rendering in the Long Count is 220.127.116.11.18 6 Eznab, which equates to September 5, 32 B.C.
The third example of an early Long Count date comes from Guatemalan Soconusco, where a stela was uncovered at the site of El Baúl in 1923 by T. T. Waterman. His reading of what has come to be called Stela 1 was "corrected" by the German archaeologist Lehman in 1926, and refined further by Michael Coe in 1957. The latter reads it as 18.104.22.168.12 12 Eb, which equates to March 6, A.D. 37. John Graham, however, proposed in 1978 that it should be read as 22.214.171.124.12, which makes its equivalent date July 21, A.D. 11, instead. At the nearby site of Abaj Takalik, two additional early Long Count dates were discovered on a monument labeled Stela 5 in 1978. The first of these Graham reads as 126.96.36.199.15, which is equivalent to May 22, A.D. 103, and the second as 188.8.131.52.11, which equates to June 6, A.D. 126. Graham also believes that the inscription on Monument 2, which was found at Abaj Takalik in 1925, is calendrical as well; however, in the reproduction of this inscription which appears in Adams (1991, 94) the only clear-cut bar-and-dot numeral to be seen is a single numeral 11 at its far left. Graham's interpretation raises the entire issue of how Olmec numerals were originally written: Were they always necessarily dots and bars? I find this question of special interest, because in the first volume published on the monuments of Izapa (Norman, 1973), no mention was made of any calendrical inscriptions having been found at that site -- perhaps the more accurate term should be "recognized." As Norman's second volume was nearing completion, he realized that "most of the monuments, whether carved or plain, have a calendrical function" (1976, 4), although my paper suggesting this possibility is not cited in his otherwise extensive review of the literature. When a third publication on Izapan monuments by Lowe, Lee, and Martinez appeared in 1982 (following by almost a decade the publication of my article in Science pinpointing Izapa as the birthplace of the calendar), it is conceded that the site's "sculptural inventory ... make it likely that this center's participation was important in the formation of Mesoamerican religion and the ritual calendar" (299). (Interestingly, this time my work was cited in the bibliography but not without making the point that I was "anticipated" in my hypothesis "much earlier" by, among others, Rafael Girard . Yet, when one consults the reference to Girard in the same bibliography, it is conceded that he made no mention of Izapa . Girard, a Guatemalan, seems to have preferred to trace the birthplace of the calendar to a site in his own country, perhaps for reasons of nationalism.) However, none of the numerous "calendrical" monuments which Lowe illustrates and describes use the conventional bar-and-dot notation for numerals. If he is correct, then the obvious implication is that, while the calendars may well have been devised at Izapa, the numerical system used for recording them must have been the later invention of some priest elsewhere.
Early in this century a strange little statuette looking rather like a duck-billed platypus, but with an unmistakable Maya Long Count date on one side, was found in the Tuxtla Mountains. Bearing a date of 184.108.40.206.17 8 Caban 15 Kankin, the so-called "Tuxtla Statuette" posed one of the first "shocks" to the "Mayanistas" because its date -- equated to March 15, A.D. 162 -- was a full 130 years older than any Long Count date found within the Classic Maya area itself However, because it was scarcely more than 20 cm (8 in.) tall, it was immediately classed as "art mobilier" by the "Mayanistas," implying, of course, that it could still have been Maya in origin even if it had been found in a distinctly non-Maya geographical area.
The most recent find containing Long Count dates was made in 1986 when a 2.5-m (8-ft) stone was fished out of the Río Acula in central Veracruz state. Now known as the La Mojarra stela in commemoration of the little fishing village where it was brought ashore, its two Long Count dates have been transcribed as 220.127.116.11.5, which equates to May 22, A.D. 143, and as 18.104.22.168.7, which is equivalent to July 14, A.D. 156.
According to the decipherment by Kaufman and Justeson, the inscription purports to describe the accession to power of a chieftain called "Harvest Mountain Lord" on the first date and his successful quashing of a rebellion led by his brother-in-law on the second date. Of special interest from a calendrical point of view is the fact that the two dates found on the La Mojarra stela begin with the day-number and day-name in the sacred almanac and end with the day-number and day-name in the secular calendar, unlike later Maya practice which placed the day-nurnbers and day-names of both the secular and sacred counts at the conclusion of the inscription. Thus, in the first of the two dates the glyph for 13 Kayab precedes the Long Count notation of 22.214.171.124.5, which in turn is followed by the glyph for 3 Chicchan; in each instance the numerals are shown to the right of their respective name-glyphs. In the second date the glyph for 15 Pop precedes the Long Count notation of 126.96.36.199.7, but here the numeral appears to the left of the name-glyph. Following this Long Count notation is the day-name glyph for Manik, but because the stone has been effaced to the left of it, what should have been the number five (i.e., a bar), in keeping with the pattern described above, is missing.
The development and use of the Long Count marks a quantum leap forward in mathematical sophistication among the peoples of Mesoamerica. It was developed in 236 B.C. by the 0lmecs, and during the Formative Period its use was restricted to a belt running from Soconusco through the Chiapas highlands into the Gulf coastal plain of Mexico.
To summarize the eight early, recognizably Long Count inscriptions, then, we find that one occurred on an artifact which was "movable" and hence can probably be expected to shed little light on the geographic origins of the Long Count. The remaining seven inscriptions are all found on relatively massive stone stelae which are unlikely to have been moved far from where they were carved, and therefore must be taken into account. Because two dates are found on each of two different stelae, the sample consists of six carved monuments in all. Of these, two were found in Guatemalan Soconusco and three were found in the Olmec area of central Veracruz, with the remaining one coming from the Grijalva Depression about halfway in between. Because of this distribution, it would be difficult to make a case for the Long Count having originated at either end of this Olmec axis, but it is clear even from the small sample at hand that a lively interchange of ideas was moving back and forth across the Tehuantepec Gap as early as the second century B.C.