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Mayan Astronomy

Note 10: The Maya Long Count, the Calendar Round, and the Dresden Codex Eclipse Table. 6/18/99

At some point during the Classic Period, a point in time which cannot be calculated precisely now, Maya astronomers created what is known as the Long Count (LC) notation. The LC was formulated by combining five cumulative periods of temporal reckoning into a single numerical statement that counted a total of 1,872,000 days. The smallest unit was a single day called Kin. Single days were grouped together in "months," called Uinal, which contained 20 days each. 18 Uinal were then counted to form the next grouping of days, called Tun, which held 360 days altogether. 20 Tun were then combined to form the Katun, which held 7,200 days each. 20 Katun counted out the Baktun which held 144,000 days. In all, the Mayas counted out 13 Baktun in the LC. The five-place notational system is calculated from right to left with the smallest number of days (kin) in the first place on the right. After that, uinal are recorded in the second place, with tun (third place), katun (fourth place), and baktun (fifth place on the far left), completing the count. An example of the notation would be the base-day of the Dresden Codex Eclipse Table 9.16.4.10.8. Added to this numerical expression, and to every other notation of its kind, was a day-name taken in sequence from the Calendar Round (CR). In this case the CR day-name fixed to this notation was 12 Lamat 1 Muan.

The combination of LC notation and CR day-name was absolutely determined by a continuous and unbroken count from the zero-base day of the LC, which was written as 13.0.0.0.0 4 Ahau 8 Cumku, and which occurred in the distant past calculated back from the Maya Classic Period. The LC notation preserves the exact number of days that separates any contemporary day (9.16.4.10.8 12 Lamat 1 Muan) in Maya time from the zero-base day. The Eclipse Table date counts its position in the following calculation:

9 X 144,000 = 1,296,000 days (plus)

16 X 7,200 = 115,200 days (plus)

4 X 360 = 1,440 days (plus)

10 X 20 = 200 days (plus)

8 X 1 = 8 days;

for a total of exactly 1,412,848 days after the zero-base day of the Maya calendrical notation. Every Maya LC notation is calculated in this same way and every date is fixed in time by the precise number of days that have passed to reach its position from the zero-base day.

There is no explanation available to us now as to why the Mayas chose the CR day-name 4 Ahau 8 Cumku as a point in time where the zero-base day of the LC count began its sequence in tandem with the 18,980-day list of CR day-names. As far as we know, that choice was completely arbitrary in the sense that the Mayas could have used any day-name in the CR list as a point of departure for the LC. Quite obviously, of course, that choice was guided by considerations, probably connected to the spirit-powers associated with the numbers 4 and 8 and with the names Ahau and Cumku, which we have no way of comprehending now. Even if the choice also involved, as it probably did, a purely astronomical consideration, the location in the sky of the sun, moon, and/or visible planets against the stellar background, for instance, we are still pretty much at a loss to explain why one thing and not another guided that initializing choice because the fact is that celestial objects were also considered to be manifestations or embodiments of spirit-power. Once the choice of 4 Ahau 8 Cumku was made, everything else, from zero-base day to zero-base day 1,872,000 days later, was absolutely fixed in a predetermined and inescapable place relative to both the LC notation and the concurrent CR day-name that identified its location in the 13-Baktun count.

An obvious reality here, though one most people might not recognize immediately, is the fact that, if the Mayas fixed the astronomical position of the zero-base day retrospectively from the middle of the Classic Period, which seems a reasonable assumption to make, so that it coincided with a particular kind of celestial configuration, and if both LC and CR were developed from, and were used to express, certain kinds of celestial periods, which is also a reasonable assumption to make, then the calendrical sequence itself would have counted out cyclical periods of celestial motion as a simple matter of course over long periods of time depending on how accurately the initial, formulating intervals of time coincided with actual celestial motion. Achieving an accurate measure of celestial interaction of the kind I am suggesting here would have taken many hundreds of years to accomplish and there is significant evidence that the people of Mesoamerica worked at this kind of task for several thousand years, from at least as early as 1500 B. C. when the first sign of using 260-day intervals appears in Olmec civilization.

A curious fact emerges when one analyzes the numerical relationship between the LC notation and the CR day-name list that completes its expression of Maya time. Counting down from the zero-base day at even intervals of the CR (18,980 days per extension), which carries one forward from the first occurrence of 4 Ahau 8 Cumku to each successive repetition of the day-name, a total of 98 CRs are consumed before a point is reached where there is less than one complete CR remaining before the next zero-base day is reached. The difference between 98 CR intervals and the total length of the LC notation at its 13-Baktun termination is equal to 11,960 days. This interval in turn is equivalent to the exact length of the Dresden Codex Eclipse Table.

This fact may or may not be the result of intentional design since there are several other reasons why Maya astronomers may have chosen the 13 Baktun interval for the notational system. 13 is an important value in Maya astronomy specifically and also has significant symbolic and spiritual meaning. Since 360 was used to determine the length of the LC, the ultimate choice for how long to allow it to run before termination was probably determined by a value that would count out an even number of tzolkins at completion (7,200 X 260 = 1,872,000 days). At the same time, the interval was not a multiple of 365. This means, of course, that a second sequence of 13 Baktuns would begin on the same almanac day-name (4 Ahau), even if it would have a different Haab name (3 Kankin instead of 8 Cumku) at the beginning of a second sequence.

The approach I want to take in resolving this problem is to assume that the 11,960-day difference between the 13-Baktun interval and the accumulation of 98 Calendar Rounds was, in fact, the primary consideration motivating the several choices facing Maya astronomers as they developed their calendrical system. In order to make this kind of argument, based on actual astronomical data, it is necessary to use a correlation number that fixes the Maya calendrical system to European methods of calculating time because all available astronomical data is preserved according to Eurocentric paradigms. Since the Goodman-Martinez-Thompson correlation has numerous flaws associated with its development, which have been discussed elsewhere in this document, especially with respect to eclipse occurrences in the Dresden Codex, I prefer to use a correlation number that corrects those flaws in order to demonstrate how the Mayas might have created the LC with its 11,960-day differential from an even number of CR sequences as it was counted by them in real time. The zero-base day in the correlation used here occurred on April 29, 3171 B. C., which is about 58 years earlier than the GMT, and is identified by Julian Day Number 563334.

Counting through the sequence of notations and CR day-names from the zero-base day the last 4 Ahau 8 Cumku prior to the termination of the sequence occurred on November 15, 1922. On that day the moon was about 3.5 days away from its new moon position and was not entering an eclipse event at the time. 11.960 days later the lunar position was about the same on August 14, 1955. The day-name for that position would have been 4 Ahau 3 Kankin and the 13-Buktun sequence would have reached its termination point. The fact that the lunar-solar relationship at the end of the sequence sheds no light on the eclipse interval of 11,960 can be taken in two ways. On the one hand, I can conclude that the difference between the LC notation and the CR sequence as they are counted out in real time has no particular significance apart from being an interesting coincidence. A different kind of argument can be made, however, when one recognizes the fact that eclipse intervals are not exactly precise in whole number extensions of the kind the Mayas used and one should not expect a projection of some 1,250 years to prove accurate in terms of an eclipse position made from the Classic Period into the twentieth century. This statement, of course, rests on the assumption that an eclipse position can be verified during the Classic Period that can be shown to conform to the expectation that the differential of 11,960 between LC and CR actually served to identify eclipse positions in real time for Maya astronomers.

This is, in fact, the case. During the time the Mayas were developing their eclipse table, in the seventh century say, 4 Ahau 8 Cumku fell on the European calendrical day September 10, 675 A. D. counted down from the zero-base day after exactly 74 Calendar Round intervals from the first occurrence of the day-name in 3171 B. C. In LC notation the day would be listed as 9.15.1.8.0 4 Ahau 8 Cumku. For the sake of verification, the difference between the Julian Day Number for the zero-base day (563334) and the one for September 10, 675 (1967854) is 1,404,520 days. Calculating the LC position, one would find that

9 X 144000 = 1,296,000 days (plus)

15 X 7,200 = 108,000 days (plus)

1 X 360 = 360 days (plus)

8 X 20 = 160 days (plus)

0 X 1 = 0 days,

equals a total of 1,404,520 days. According to Bao-Lin Liu and Alan D. Fiala, in Canon of Lunar Eclipses, 1500 B.C.--A.D. 3000 (Richmond: Willmann-Bell, 1992), a lunar eclipse occurred on September 9, 675 A.D. between the hours of 19:51 and 21:42 PM (GMT). 11,960 days later, on June 8, 708 A. D., when the LC count had reached 9.16.14.12.0 4 Ahau 3 Kankin (1,416,480 days after the zero-base day), a second lunar eclipse occurred between the hours of 0:10 and 1:28 AM. This second eclipse is significant because it occupies the 21st eclipse position in the Dresden Codex Eclipse Table (p 56a, col E) after the Classic Period base-day established by this correlation at 9.16.4.10.8 12 Lamat 1 Muan on June 29, 698 A.D. The base-day eclipse, according to Liu and Fiala, occurred between the hours of 2:22 and 3:29 AM (GMT).

The point that can be made here is that while eclipses did not occur in this kind of sequence at the termination point of the relationship between the LC and the CR, in 1922 (November 15) and 1955 (August 14) respectively, at a time when Maya astronomers would not have been able to verify the accuracy of their calculations under any circumstances, it was possible during the Classic Period, when the Mayas actually created and used the Eclipse Table, to do precisely that, since real eclipses did occur in real time on the day-names specified both by the 11,960-day differential between the LC and the CR and by the sequence of eclipses they specified in the Dresden Codex Eclipse Table. Having this symbolic expression come out right during the Classic Period, on the day-names specified, would have been far more valuable, far more meaningful, to them than it would have been for it to work in the same way 1,250 years later when the sequence of the relationship was resolved at its terminal point. Whether the Mayas knew that their eclipse sequence would ultimately fail to express the desired goal at the end of time is a question we cannot answer with any certainty now but it does seem clear that they would have been able to perceive the relationship between 9.15.1.8.0 4 Ahau 8 Cumku and 9.16.14.12.0 4 Ahau 3 Kankin when they wrote the Eclipse Table itself because that relationship was simply a matter of observational reality inside the limits of the calendrical system they used every day of their collective lives. It was, to them, self-evident.

There is a chicken-and-egg question here, of course; that is, which came first, the Eclipse Table, or the relationship between the LC and CR counts? They are clearly related to each other, if not interdependent, since one so precisely reflects the other. The idea that this could be a coincidence, that it just happens to work out this way in real time at the precise historical moment when the Eclipse Table came into existence in the context of an already fabricated calendrical expression which fixes day-names and numerical expressions of them into absolutely rigid relationships, is literally impossible. The LC and CR differential at 11,960 must have evolved out of the development of the Eclipse Table because there would have been no way to change the day-names as they were being counted during the Classic Period to match these two eclipse occurrences. The most likely possibility at this point in our understanding of this technology is that the two systems were created simultaneously with the differential being fixed by the length of the Eclipse Table and the appropriate day-names being put in place retrospectively from the Classic Period back in time to the zero-base day. In any event, the minds that made this thing, and clearly more than one person is responsible for it, cannot be termed "primitive" or "savage."

To say what is only obvious: the people who attempted to destroy this technology at the beginning of the sixteenth century were something more than just barbaric.

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