Eclipses, 2012, The Number Zero, Gliding, and the Mayan Long Count Calendar

As the Maya observed the skies they noticed that the lunar and solar eclipses occurred at certain positions in the 260-day tzolk'in calendar. This is because the eclipse period coincides with 260 days. Eclipse seasons occur each period of 173.31 days. Three of these eclipse periods equals 519.93 days or almost 520 - two tzolk'in cycles.

The Maya noticed that the eclipses took place at three specific zones or seasons within the tzolk'in. Each season was about 33 days long - the eclipse season. Every 173.31 days the eclipses would take place in one of the tzolk'in eclipse seasons.

For example, between April 25 and May 25, 2013, two lunar and one solar eclipses will take place in the tzolk'in season at the bottom of the figure below, in the weeks Chichan-Etz'nab'-B'atz-Kach (Chikchan-Etz'nab-Chuen-Kan). (Note: for dates post 1582 CE I use the GMT correlation of 584188 or -95.) Then there will be a period of about five months with no eclipses. During this period the tzolk'in will progress through the tzolk'in eclipse season that begins in Ahmok (Cib) week - but no eclipses occur then because eclipses occur only every other time through the tzolk'in eclipse seasons.

Between October 18 and November 3, 2013, there will be one lunar eclipse and one solar eclipse. This takes place in the tzolk'in eclipse season of Ch'i'-Ahchuk-B'ahk' (Manik'-Ahaw-Ben). Then there will be a period of about five months with no eclipses. During this period the tzolk'in will progress through the tzolk'in eclipse season that begins in Chichan week. Finally between April 15 and April 29, 2014, there will be one lunar eclipse and one solar eclipse. This takes place in the tzolk'in eclipse season of Ahmok-Tojmar-Ik'ar-Tz'ikin (Cib-Muluk-Ik'-Men).

The Eclipse Seasons and the Tzolk'in

Eclipses are only visible in a portion of the earth. Lunar eclipses over a broader area and solar eclipses only along a narrow ribbon, although a broader area can see the partial effects of the eclipse. The Maya noticed that eclipses were more commonly visible in Central America in a certain tzolk'in eclipse season - for example at our current time that is the one that is currently in the tzolk'in weeks of Ch'i'-Ahchuk-B'ahk'. Over hundreds of years the eclipse visibility belts associated with each tzolk'in eclipse season rotate eastward around the globe. To be clear, not every eclipse within a given tzolk'in eclipse season is visible in the named geographic zone. But they are more often visible in that zone than in other parts of the earth.

Another observation that the Maya would have made is that every ten tzolk'in cycles (7+ years) there would be an eclipse usually just one day earlier in the tzolk'in cycle than the one seven years earlier, sometimes two days earlier. For the tzolk'in eclipse season that corresponds mostly to the Americas and the Atlantic, there are times when nine or more consecutive lunar eclipses in the ten-tzolk'in cycle are visible in Central America. This would have been sufficient for the Maya to figure out this ten-tzolkin (7 year) eclipse pattern. This cycle was studied by George van der Bergh in the 1950s and was named the "tzolkinex" by Felix Verbelen in 2001.

The table below demonstrates the cycle through the tzolkinex series beginning with the lunar eclipse in August 1962 that was in Saros cycle 147. Each consecutive eclipse in the tzolkinex is one lower in the Saros cycle, in this case ending with Saros 114 in 2197. The series begins with penumbral eclipses, then goes to partial eclipses, then total eclipses, partial eclipses again, and finally ending with penumbral eclipses. Twenty five of the 34 eclipses in this cycle were visible in Central America, either completely or partially. This tzolkinex series falls within Americas/Atlantic visibility belt, in the upper right of the tzolk'in graphic above. 

Lunar Eclipse Tzolkinex Series Beginning 1962

Date at Center of Visi- bility	Saros	Total (T) Par- tial (P) Penum- bral (N)	Visible in Central America V=yes v=par- tially	Center of Visibility Region	Tzolk'in Week
1962 Aug 15	147	N		Indian Ocean	12th of B'ahk'
1969 Sep 25	146	N		East Africa	10th of B'ahk'
1976 Nov 6	145	N		Africa	9th of B'ahk'
1983 Dec 20	144	N	V	No Atlantic	9th of B'ahk'
1991 Jan 30	143	N	V	Cent America	7th of B'ahk'
1998 Mar 13	142	N	V	Venezuela	6th of B'ahk'
2005 Apr 24	141	N	V	So Pacific	5th of B'ahk'
2012 June 4	140	P	v	So Pacific	3rd of B'ahk'
2019 July 16	139	P		So Africa	1 B'ahk'
2026 Aug 28	138	P	V	So America	1 B'ahk'
2033 Oct 8	137	T	V	Pacific	12th of Ahchuk
2040 Nov 18	136	T		India	10th of Ahchuk
2048 Jan 1	135	T	V	Central America	10th of Ahchuk
2055 Feb 11	134	T		Africa	8th of Ahchuk
2062 Mar 25	133	T	V	Surinam	7th of Ahchuk
2069 May 6	132	T	v	So Pacific	6th of Ahchuk
2076 Jun 17	131	T	v	Brazil	5th of Ahchuk
2083 Jul 29	130	T	v	So Atlantic	4th of Ahchuk
2090 Sep 8	129	T	v	DR Congo	1 Ahchuk
2097 Oct 21	128	T	v	Atlantic	1 Ahchuk
2104 Dec 2	127	P	V	Cuba	12th of Ch'ih
2112 Jan 14	126	P	v	West Africa	11th of Ch'ih
2119 Feb 25	125	T	v	Pacific	10th of Ch'ih
2126 Apr 7	124	T		Indonesia	8th of Ch'ih
2133 May 19	123	P	v	Brazil	7th of Ch'ih
2140 Jun 30	122	P	V	So Pacific	6th of Ch'ih
2147 Aug 11	121	P		Indonesia	4th of Ch'ih
2154 Sep 21	120	N		South Indian	2nd of Ch'ih
2161 Nov 3	119	N	V	Caribbean	2nd of Ch'ih
2168 Dec 14	118	N	v	No Africa	13th of B'ahram
2176 Jan 26	117	N	V	Atlantic	12th of B'ahram
2183 Mar 9	116	N	V	Pacific	11th of B'ahram
2190 Apr 20	115	N	V	Pacific	10th of B'ahram
2197 May 31	114	N	V	Pacific	8th of B'ahram

At any one time there are about 15 active lunar eclipse tzolkinex series and about 15 active solar eclipse series. Generally there are five tzolkinex in each tzolk'in visibility zone and they remain in that zone for the life of the series. The tzolkinex series are spread out evenly in the tzolk'in visibility zones, one near the beginning of each zone (most clockwise), one near the end of each zone (most counter-clockwise), and the remainder spread out in the middle. Each tzolkinex has a duration of about 250 years. A new tzolk'in eclipse series begins every 40 to 54 years in each of the three eclipse visibility zones.

The tzolkinex was one way that the Maya predicted the timing of both lunar and solar eclipses. But there was some variability as one can see in the table above. They found another cycle that was much more accurate in predicting timing - the 46 tzolk'in cycle. This is also known as the Triple Tritos cycle (32.745 years or 11,959.89 days) and is .11 days short of being exactly 46 tzolk'in cycles. This cycle is demonstrated in the Dresden Codex, a pre-Hispanic Mayan scientific document. The 46 tzolk'in cycles are equivalent to 405 lunations.

For the Maya it would have been important to predict the the placement of the eclipses, not only their timing. The Maya did this using the Saros cycles. By tracking the placement of eclipses by their Saros cycle the Maya would have been able to have a good idea of the placement of future eclipses. Each successive eclipse in a Saros cycle is about 120 degrees east of the previous one. This means that every third eclipse in a Saros cycle, also called the Triple Saros, is located at approximately the same place on the globe.

The Triple Saros is a period of 54.090 years. Every other eclipse in the tzolkinex starts in the northern polar region, while the other starts near the south pole. Over the more than a thousand years of the Triple Saros cycle, the center point of the eclipse moves toward the opposite pole from where it started. The center point of the eclipses will often move to the east at some point in the series as well. However, when the eclipse center point is near either of the poles successive eclipses in the Triple Saros cycle tend to move westward rather than eastward.

To illustrate the movement of the path of solar eclipses with each successive Triple Saros cycle eclipse I will show the maps of eight successive solar eclipses in the Triple Saros cycle of Saros 141. This cycle is in the North American - Atlantic visibility zone. It started in the north polar region and moves to the south. I have skipped displaying the partial eclipses at each of the polar regions. Generally all of the central (non-polar) eclipses of a Triple Saros cycle are either annular or total. All of the eclipses for the series displayed here are annular.

Saros 141 Solar Eclipse Cycle (Triple Saros)

Sep 17, 1811 Annular, 43N 86W Center, 13th of B'ahk, 12.9.16.1.5

Oct 19, 1865 Annular, 21N 60W Center, 9th of B'ahk, 12.12.10.17.1

Nov 22, 1919 Annular, 7N 49W Center, 5th of B'ahk, 12.15.5.14.17

Dec 24, 1973 Annular, 1N 48W Center, 1 B'ahk, 12.18.0.12.13

Jan 26, 2028 Annular, 3N 52W Center, 10th of Ahchuk, 0.0.15.10.9

Feb 27, 2082 Annular, 9N 47W Center, 6th of Ahchuk, 0.3.10.8.5

Apr 1, 2136 Annular, 16N 26W Center, 2nd of Ahchuk, 0.6.5.6.1

May 4, 2190 Annular, 19N 15E Center, 11th of Ch'i', 0.9.0.3.17

I believe that the Maya began to track not just the timing but also the placement of solar eclipses by utilizing the Triple Saros cycle. Looking at the cycle above one can see that the first six would not have been too difficult to track. The eclipses move southward and eastward about 5 to 10 degrees with each successive eclipse. The main challenges would be to identify the first one in the series, to know when the right new moon was coming up, and to keep track of the placement of the previous eclipse, considering that it would have been 54 years earlier and that there were over 100 active solar eclipse cycles at any time.

In order to know where to look for the first one in the triple saros cycle (or first one that was not polar), the Maya would have known if it was "dropping" from the north (or south) pole. They also would have had a clue if it was an eclipse that is typically in the Americas/Atlantic zone. (Note the zones change over time.) But that still leaves thousands of miles to cover. I think this is where talking with neighboring peoples came in - inquiring if the solar eclipse had been seen there. They likely spent several months or years doing reconnaissance.

The second challenge was to track timing of each successive eclipse in the Triple Saros cycle. Every 669 lunations is a Triple Saros eclipse - that would have been one way to track it. Another way to track would have been the long count calendar. There is a period of 0.2.14.15.16 between each successive eclipse. This would have required writing down (or using sticks and balls in a protected space) the date of the previous eclipse. The Maya may have been tracking dates much earlier than commonly believed. In addition each successive eclipse falls four days earlier in the tzolk'in than the previous one.

The third challenge is to keep track of the placement of the previous eclipse, assuming that they had tracked it. Living memory would be the easiest way to track, although it could become confusing if one person is attempting to remember several different eclipses over several years. Also, there are 54 years between Triple Saros eclipses and given life spans it would not have been common for a person to live long enough to see two successive Triple Saros eclipses. An oral tradition could have been passed from one generation to the next with a description of where the previous eclipse had been seen. But I think that the most likely way that Maya tracked eclipse paths was through mapping it. This could be maps on rocks or, more likely, creating a map on bark strips.

I believe that ley lines might be the tracing of the path of solar eclipses across the land by the ancient ones. This practice could have been done in both the Americas and the eastern hemisphere. If so, ley lines should be thought of as curves rather than lines.

The three tzolk'in visibility zones presented near the beginning of this post move slowly backward - counter-clockwise - through the tzolk'in over hundreds - thousands - of years. This is because, as I mentioned, three eclipse seasons equal 519.93 days, which is just short of two tzolk'in cycles, or 520 days. The difference will total one day every 19.71 years. Each day in the tzolk'in cycle repeats every 20 days and it would take 394 years for the tzolk'in eclipse season to recess 20 days in the tzolk'in.

Tracking the tzolk'in eclipse season would have been important because it would have been an easy way over very long periods of time to pass on the knowledge of eclipse tracking, especially how to locate eclipses. Plus it tied the most significant regular astronomical feature - the eclipse - to the sacred calendar of the Maya that had been in use since at least 8200 BCE, the tzolk'in.

Sometime before 3114 BCE the Maya were tracking the timing of the eclipse seasons through the tzolk'in eclipse season and built the long count calendar to track this. The long count calendar is built on the following mathematics: 13.20.20.18.20. Starting from the right-hand side, there are 20 k'ins (days) in one uinal, then 18 uinals in one tun, then 20 tuns in one katun, 20 katuns in one baktun, and 13 baktun before the cycle starts over again.

	Baktun	Katun	Tun	Uinal	K'in
Number in Cycle	13	20	20	18	20
Days	1,872,000	144,000	7,200	360	20
Years	5,125.3	394.3	19.7	1.0
Days of Precession with the Tzolk'in	260	20	1	0.05
Tzolk'in Years	7,200	553.85	27.69	1.38	0.08

With the completion of 20 tuns (one katun) the tzolk'in eclipse seasons have moved backward one day in the tzolk'in. This happens every 19.7 years. Today this calendar is not exact, it takes slightly longer than 19.7 years for the tzolk'in eclipse season to precess one day. But this changes over time and seems quite likely that the calculation was exact in 3114 BCE. The historical eclipse dates listed in the NASA eclipse website correlates with a faster pace of change in the length of the eclipse year than what the Mayan long-count calendar would suggest.

Looking at the table above, one notices that there are 260 katuns in one complete cycle of the long-count calendar (20 katuns in each of 13 baktuns). This means that the tzolk'in eclipse seasons would complete exactly one round through the tzolk'in in the 5,125.3 years of the long-count, at least it would be exact if the eclipse year would have remained constant.

In one baktun the tzolk'in eclipse seasons move back in the tzolk'in exactly 20 days to the next occurrence of the same day sign. This would be easier to remember if the Maya were keying one day in the tzolk'in to track the tzolk'in eclipse seasons. There is some evidence that they were using the Ahmok day sign (Cib) to do this. A second meaning for the Ahmok day sign comes from ahmo' which means the large bird man or the falcon man. This helps explain the Aztec sign of the vulture for this day. The Maya believe that a falcon god or falcon man flies up to the sun and eats the sun thus causing a solar eclipse (or alternately to the moon for a lunar eclipse). The tzolk'in glyph (left) for the Ahmok day sign has been described as an empty shell, which symbolizes both an eclipse and the number zero.

At Palenque and several other sites are inscriptions that describe the beginning of the long count calendar, mistakenly called the creation date by some. These inscriptions describe four important events that relate to the beginning of the long-count calendar:

• the tracking of eclipses that helped confirm the arrangement of the long-count calendar;
• the invention of the zero digit, essential for the long-count calendar;
• the completion of one of the largest public works of the Maya coinciding with the long-count calendar initiation;
• gliding - the falcon man who eats the sun or moon to cause the eclipse.

Tracking eclipses

The Palenque inscriptions list the birth of First Father or Father Sun in 3122 BCE and the birth of First Goddess or Moon Goddess later in 3121 BCE. It is likely that these are referring to a solar eclipse and a lunar eclipse, respectively. The date of the Father Sun event was  12.19.11.13.0 or March 1, 3122 BCE (correlation 584178) and was a new moon according to the Solex astronomy program, meaning it could have been a solar eclipse. Based on the NASA eclipse projections it would not have been an eclipse but those projections assume a certain rate of change in the length of the eclipse year. On the other hand, based on the tzolk'in eclipse seasons, that date should be an eclipse.

The Moon Goddess date of 12.19.13.4.0 or August 24, 3121 BCE was not a full moon, although three days later there was a full moon which likely would have been a lunar eclipse. The Moon Goddess date was 540 days after the Sun Father date, or twice through the tzolk'in plus 20 days. Both fell on Ahchuk (Ahaw) days, which means "the observer". Given its placement in the tzolk'in eclipse season it is possible that the lunar eclipse three days after the Moon Goddess was the beginning of a tzolkinex cycle and perhaps the beginning of a new lunar saros cycle. The Moon Goddess is called Lady Sak, which could mean either the White Lady (Moon Goddess) or the Search Lady, as in searching for the eclipse. Likely it means both.

The two eclipses confirmed the timing of the tzolk'in eclipse season. Once this was confirmed, the Maya waited only for the right astronomical event, which was the moon-Venus-Jupiter conjunction of April 27-28, 3114 BCE, which is when the long-count calendar began.

Invention of the Zero Digit

The Vase of the Seven Gods states that "Black its Center" was put in order on 0.0.0.0.0, the beginning calendar date. Several gods or spirits put Black its Center in order. This could be referring to eclipses but I think it is more likely that it is talking about the invention of the number zero. It would have been necessary to have the zero digit in order to create the long-count calendar. In other words, the number zero was created in order to have the math necessary to track eclipses.

Completion of a Public Works Project

The Palenque inscription lists an event that took place less than two years after the start of the long-count calendar, on October 21, 3112 BCE. Usually this is translated at the dedication of the World Tree of the North. However the language used makes it likely that this event was the dedication of a physical work not an astronomical concept. From my own research I can conclude that it was a grand public work, possibly the greatest public work of the Maya. I will be describing this public work at a later time.

Gliding

Palenque also records three events (often translated as the birth of gods GI, GII, and GIII) in July 2360 BCE: Event GI on July 6, 2360 (1.18.5.3.2), event GIII on July 10, 2360 (1.18.5.3.6), and event GII on July 24, 2360 (1.18.5.4.0). These events are said to take place at Matawil. They are referenced right after the 3122 and 3121 eclipses so these events are associated with eclipses. The translation of Matawil is revealing:

matz - wrapping around
wil - wing

"Wrapping wings around." In a similar vein, one of the names for the First Goddess, the Moon Goddess is Muwaan Mat:

muahn - hawk, falcon
matz - wrapping around

"Wrapping a hawk around". Here one can imagine the mythical image of the falcon man who flies up to moon and eats the moon (or sun) causing the eclipse. The Ch'orti' call this falcon man ahkilis. They created a flight suit made of hawk or falcon wings and with that flew or glided. The beginning date of Mayan gliding, or perhaps it was the beginning of the falcon man myth, appears to be 2360 BCE, according to the Palenque records.

The event (god) called GIII was born four days after GI - four days after the invention of the wings. It is also called Mah K'ina.

mah - bad, evil
k'ina - hot water

"Evil hot water," which I interpret to mean the boiling lava of an active volcano. This appears to say that four days after the first flight, a flight was attempted off a volcano where the flier landed inside the volcano. A tragedy. Probably adjustments were made to the wings and corrected by 14 days later, the event of GII.

GII was the last of the 2360 BCE events. The Palenque Temple of the Foliated Cross is dedicated to GII, also called God K or Kawiil:

kah - beginning
wiil - wing

"Beginning of the wing."

The significance of 2012 when viewed through the eclipse lens is that we have the same or very similar tzolk'in eclipse seasons in 2012-13 as were present in 3114 BCE. This would have had a lot of meaning in 3114 BCE. This would have been at least part of the significance of 2012 for the ancient Maya.