Mayan Astronomy & Mythology – A Popol Vuh Story Decoded: Zipacna & the 400 Boys
Keith M. Hunter
Mayan Astronomy Encoded in Mythology
Mayan mythology shares great similarities with other mythologies around the world. In general when one reads of such stories about gods and goddesses and their exploits, one is presented with a set of tales that stretch the imagination. Such stories appear quite often to be ludicrous in their presentation. However, behind such stories there is often a very profound truth. Many stories from ancient cultures that relate the deeds of heroes or other such men or women of note, including fantastical magical beings, oftentimes represent a metaphor behind which is a very solid historical truth, or principle of nature. Invariably, many tales as told by the Mayan people as indeed are contained in perhaps their most prominent work, the Popol Vuh, have a distinct astronomical bent.
They encode knowledge, and knowledge of a profound nature: the principles of basic Mayan astronomy and Mayan calendar cycles.
Carefully decoded, certain critically important Mayan myths reveal the truth of the matter that this particular Central American civilisation was in possession of highly advanced scientific knowledge.
Popol Vuh Mythology & Mayan Astronomy
In this particular essay I wish to give the reader what may be termed a ‘classic example’ of how to correctly understand a key story as is contained within the Mayan Popol Vuh. It is a particular story that on the face of it appears superfluous and of no real consequence. However, correctly decoded, it reveals that the Mayans were indeed possessed of great astronomical knowledge to rival that of the present age, and possessed values of various astronomical orbital periods to a level of accuracy that indeed is on par with the accuracy of modern astronomers of the late 20th century.
The story in question relates to a particular incident in the life of a certain character of note as detailed within the Popol Vuh. The character’s name is Zipacna. What follows is a brief citation from the Popol Vuh as translated by Dennis Tedlock. The analysis as will follow on will illustrate the solution to the tale and ground it firmly within the scientific-astronomical realm:
And here are the deeds of Zipacna, the first son of Seven Macaw.
The Solution to the Mayan Story of Zipacna and the 400 Boys
On the face of it the above story appears to be quite inconsequential. However, correctly decoded the above story in actual fact implies that the ancient Maya were able to derive an orbital period value for the Earth tropical year to an extreme level of accuracy, and also a value for the time cycle that captures recurring synodic conjunctions between the Earth and Mercury.
In order to explain this most fully, one needs to understand something about the basics of calendar systems as a whole. Calendar systems are all about harmony. They are premised upon the question: how many times does one event fit within the space of another event? One may consider the Earth's orbital period about the sun. One complete orbit about the sun is one event or one cycle. But then one may consider also the Earth rotating on its own axis. This indeed is another event or celestial cycle. One may thus pose the question of how many times the Earth rotates on its axis in the space of one cycle about the sun. The answer to this question is of course the length of the Earth tropical year – expressed in solar days. And the length of this time cycle, as has been stated previously in other essays, is 365.2421840 solar days.
Now indeed, this particular value is just slightly less than precisely 365 and a quarter days (365.25). From a calendrical perspective the basic Earth year of 365.25 days is derived from a very simple four-year corrective mechanism. This is the basic system as used in Western calendars that makes use of a leap year every four years, where one has three years of 365 days followed by a fourth year of 366 days. If one adds up (365 x 3) + 366 and then divides by four, then one has derived a year of 365.25 days.
But of course we know that this is wrong. We know that the length of the Earth year is just slightly less than an exact 365.25 days. Thus we would need a further correction to try to refine the Earth year to an even more exacting standard. And so the question is posed, when would be the optimum time for a further correction in addition to a standard leap year correction every four years? The answer to this question is readily to be had and indeed was known to the ancients.
In addition to a simple leap year every four years, in order to refine the Earth tropical year to a more exacting standard and capture the true value for its length, one must have an additional one day correction to the basic leap year formula every 128 years.
Refining the Earth Tropical Year to an Exacting Standard
If one uses a basic leap year correction every four years, from which one derives an Earth tropical year value of 365.25 days, then using this value as the length of an Earth year, one may calculate the number of days within 128 such years:
365.25 x 128 = 46752 days
Now indeed, if one were to use what has been determined by modern astronomers to be a very accurate value for the Earth tropical year, of 365.2421840 days, and multiply this figure by 128, one gets a value that is in fact most harmonious with respect to a complete number of solar days:
365.2421840 x 128 = 46750.99955 days
As can be seen, this new value is almost exactly 46751 days, which is one day less than the value derived from using a basic 365.25 day year over the course of 128 years, as given above.
The implication of this is that if one were to use a basic leap year every four years continuously from some given start point, but on the 128th year, which would indeed ordinarily be classed as a leap year of 366 days – being the fourth year of the 32nd ‘batch’, one were to count instead that year as being 365 days i.e. that is to say that the 32nd four-year batch is comprised of four years equal to 365 days a piece, rather than three years of 365 days followed by a fourth year of 366 days; then in this instance, a far more refined value for the tropical year is to be had:
(((365 x 3) + 366) x 31) + (365 x 4) = 46751 days
46751 / 128 = 365.2421875 days
One can compare this with the value as determined by modern astronomers given previously, and calculate the difference:
(365.2421875 - 365.2421840) x 86400 = 0.3 seconds
Mayan Calendar Corrections
In light of the above, just what exactly then does the Mayan myth involving Zipacna and the 400 boys have to do with the Earth tropical year? The key to understanding this is the realisation that the whole story is a metaphor or allegory of how to track successive Earth-Mercury synodic conjunctions. This is to be had from a careful consideration of just why, in particular, there are 400 boys in the story. This is not an arbitrary number.
To be very clear and isolate the variables in this story, one needs to realise that Zipacna as a character is actually representative of one solar day. Also, the 400 boys are themselves representative of 400 days. In addition to this the 400 boys also represent a division sum. This will shortly become clear. For now though one needs to consider very carefully the arrangement of the Earth and Mercury with respect to successive synodic conjunctions.
To begin, it is necessary to calculate the value for the time cycle of successive Earth Mercury conjunctions. This is derived from knowing the value of the Earth orbital period and also Mercury's own orbital period. The values of both cycles are stated as follows:
From these two values one uses a very precise formula to determine the value for successive conjunctions involving both bodies:
(365.2421840 x 87.96843536) / (365.2421840 - 87.96843536) =
The farther away from the sun a planet is, the longer it takes to orbit once around the central solar body. If therefore the Earth and Mercury began in a perfect conjunction, and one were to ‘start the clock ticking’, then Mercury would race ahead in its orbit about the sun outpacing the Earth (NB: Both travel around the sun anticlockwise from a northern ‘plan view’). Whilst the Earth was still attempting to complete its first orbit about the sun Mercury would catch up with it and proceed to ‘lap’ the Earth. In doing so this would cause a new conjunction to occur between the planets, known as a synodic conjunction. This would occur after exactly 115.8774807 days, as calculated. It would not of course be a conjunction at the same place as that of the starting point conjunction, as the Earth itself would have progressed almost a third of the way into its first orbit about the sun when Mercury caught up with it.
The Mayan Astronomy Behind the Myth
A careful evaluation of the Zipacna Mayan myth reveals that they were aware of how to calculate exactly the time cycle that governs successive Earth-Mercury synodic conjunctions. This is revealed as follows:
The whole Mayan myth hinges upon the special significance of the extra one-day correction every 128 years to harmonise the Earth's orbital period with respect to a whole number of days, to achieve a most exacting level of accuracy.
In the myth Zipacna as a character is actively representative of this special one-day correction every 128 years. The hole that is dug into the ground is itself representative of an alignment of the Earth and Mercury. When Zipacna digs his side tunnel and places himself inside it just offset from the main shaft, he represents a discrepancy - in a real astronomical-calendrical sense. The 400 boys above ground waiting to place their pole into the shaft also represent a 400 day correction. Here is how the mathematics works:
1) Assuming a starting conjunction of the Earth and Mercury; employing a basic four-year cycle involving a leap year correction every fourth year, after exactly 128 years, which under this system would each equal 365.25 days precisely, one will have counted out exactly 46752 days:
365.25 x 128 = 46752 days
2) When one has achieved this figure one then makes an additional critical correction of one extra day. Zipacna represents that one day. He is the additional correction, to be subtracted from the ‘gross total’ of 46752 days:
46752 – 1 = 46751 days
3) With this new value one must now subtract another measure of days, and this indeed is why there are exactly 400 boys in the story. The next correction measure is the subtraction of exactly 400 more days. This gives a new total:
46751 – 400 = 46351 days
4) There is of course a second reason why there are 400 boys. Not only do they represent a whole number of days as a correction measure, they also are representative of a division. This is why they fall about drunk in the myth. If one takes the value of 46351 and further divides it by 400, one generates a value which is almost dead on the time value for successive Earth-Mercury synodic conjunctions:
46351 / 400 = 115.8775 days.
One can compare with the value as derived from modern astronomical observations determined previously:
(115.8775 – 115.8774807) x 86400 = 1.66 seconds discrepancy!
Mayan Astronomy in the Myth of Zipacna - In Summation
One can see then that what on the face of it appears to be a story involving a simple encounter with someone walking along a beach bumping into 400 boys attempting to erect a hut, is in fact a complex story encoding calendar corrections that allow one to accurately define a value for the Earth tropical year, including a value for the synodic conjunction period involving the Earth and Mercury. The ultimate value as derived by the two noted corrections of 46351 days, is a value that contains a whole number batch of precisely 400 such conjunctions. The completion of such a number of conjunctions is symbolised by the death of the boys at the hands of Zipacna.
As a general point to the reader one should understand then this particular explanation to be a classic example of exactly how one should approach mythological stories.
Proceed to Part 5:
The Long Count Mayan Calendar System
 Mercury Orbital Period Value cited from “The Explanatory Supplement to the Astronomical Almanac.” US Naval Observatory. Edited by P. Kenneth Seidelmann.
Page 704. (0.24084445 x 365.25 = 87.96843536 days)