The Hidden Numbers of K'awil.

Introduction

Chan-Balam of Palenque, the son of Pakal, decorated the Temple of Inscriptions with a relief sculpture of himself as a young boy, identified as the "god K'awil, a sacred being who symbolizes the embodiment of spiritual force in material objects" (Maya Cosmos, p.193). An interesting point regarding such an identification is the cited day-count related to the K'awil glyph and figures:... "the appearance of four K'awils in the 819-day count, which divides time into four quadrants, each with its own color, direction, and version of K'awil" (Maya Cosmos, p.443).

As we have been attempeting to illustrate through our analyses of the different day-counts that appear to be historically significant in ancient artwork of Mesoamerica, let us now turn our attention to a somewhat little known day-count, which appears to have a profound meaning in relation to the ancient reckoning system in general. At first glance, it would appear that the number 819 might not offer an obvious relationship to the day-counts of 260, 360, or 584, munch less to that of 225 (Venus's sidereal count). Yet, upon closer examination, it would appear that the 819 day-count, in fact, encloses or encodes, and reflects related knowledge to the very concept of the act of Creation and the numbers related to the Universe.

K'awil: 204.75

In our search to comprehend the logic of numbers that underlies the historically significant numbers cited in the glyphs and sculptures of Mesoamerica, the 819 day-count of the K'awil reference must be related to the number four: 4 K'awils: 4 quadrants. One may initially conceive of multiplying 819 by 4, obtaining thus 3276; or, one may divide 819 by 4 and obtain the fractional number 204.75.

The next step would be to observe how these numbers behave through the mediatio/duplatio method, as we have done in previous analyses. It is unnecessary to offer an exhaustive analysis of these numbers here; with a few calculations, various computational numbers and constants appear on the following list of numbers.

As of the number 819, through doubling or halving that number various numbers appear on the above list which seem to offer the beginning to a key for understanding the maya numbers of cycles. The number 6552 becomes quite obvious in reflecting the cycle numbers that are relatively significant, which are 65 and 52, when viewed separately. Let us carry out the table a little further then:

In the above presentation, we have separated the obvious cycle numbers, thereby it may be observed that sets of cycle numbers appear, as well as the constant numbers:

One may observe these sets of numbers as a key to understanding the cycle numbers and a set of constants in this manner. Furthermore, the set of numbers that we excluded from the above chart appear to have a distinct relevance among themselves. Consider the following , for example:

The fractal 25956 has been cited as a computation for precession by the maya (El Universo de Teotihuacan, p.89.) Furthermore, if one carries the 4.75 figure through the mediatio rocess, a fractal of .296875 is obtained, which is only .1575 difference from the lunar count (29.53). Harleston has maintained that the ancient maya/teotihuacanos knew the 29.53 day-count for the Earth's moon.

When we submit the 29.53 day-count to the mediatio/duplatio method, one may observe the numbers related to the Dresden Codex tables appear in relation to constant numbers (6, 12, 24, 48, 96). It would appear that such a method of cumputation allows for memorizing and learning in very simple manner the relationship of numbers and their constant. Consider the lunar day-count of 29.53, then, by halving and doubling it.

As may be observed in the above chart, the lunar phase numbers appear in their natural sequence

but, they are accompanied by a sequence of constant numbers as well, formed by the doubling of the unit .03 of the lunar count (29.53):

96 48 24 12 6 3

These constant numbers are quite significant in the historical record, and appear as counted elements in much of the ancient artwork of Mesoamerica. Numbered elements of the Aztec Calendar come to mind immediately. Also, the fact that the numbered sequence obtains with the Dresden Codex day-count number 236 (for Venus) accompanied by the constant numbers 24 would appear to have computational relevance. By knowing the numerical sequence of numbers, one could always know that the constant 24 must be considered for lunar phase computations to be exact at that level; each numerical case would apply the same reasoning regarding the corresponding constant in order to make adjustments in computations. (For a previous analysis of the Dresden Codex numbers and constant, cfr., Earth/matriX No.16.)

One should also observe on the 29.53 day-count chart, how the maya long count numbers lead off some of the fractional numbers:

In earlier essays, we have seen how the number 23400 (day-count) is significant in relation to cycle numbers:

Now, if we consider how the day-counts and year-counts were interchangeable at times, with floating decimal points and fractal, then the number 236.24, read as 23624 is simply close to one cycle of 224 days (Venus with 225 days for its sidereal orbit) above the 23400 figure:

K'AWIL: 819 and the Fractal 142857

If we then consider the lunar phase day-count as 29.53, and divide it into the day-count number 819, one might observe a number very close to the sidereal month of the moon's orbit:

The moon's sidereal orbital time today is generally cited as being around 27.32166 days, representing a difference of .4128472807, from the above computation.

But, aside from these apparently possible relationships, the number 819 seems to enshroud another significance in relation to the number seven and the fractal/fractional number 142857, which has been cited by other authors as being meaningful to ancient knowledge (West; Harleston). "Both three and seven are 'perpetual motion' numbers". Divided into unity, they divide infinitely.

The number 819 (K'awil) produces the same effect at a division of the number seven:

Hance, when we take historically significant numbers of the ancient Mesoamerican reckoning system and divide them by the number 819 or fractals/fractions thereof, then we obtain expressions of the 142857 sequence.

While in other cases, significantly historical numbers when divided by 819 show the same sequence, but in reverse order:

and, furthermore,

The enneagram (Grand Ennead) number, 142857, now appears in reverse order as the sequence 758241; direction of the numerical progression has been changed. Given that the numbers 144, 360, 936, and 1296 are multiples of 36 (or 360 fractal), we asked ourselves what might be the behavior of a list of numbers in sequence order of those multiples as of the daycounts of 360 and 225. For, in our other essays (Earth/matriX No.16), we have considered the idea that the 360/225 relation concerns the relation itself between Earth's orbital time and Venus's sidereal orbit. The historically significant Mesoamerican numbers of 144, 360, 936 and 1296 might reflect just that relationship. Therefore, consider the following list of numbers where we offer a numerical progression as of the numbers 225 and 360.

We began our count as of subtracting 360 from 1296 in order to obtain the progressive table on the left (360c); and, then, we saw that the number 144 divided the positive/negative numbers of this table, and that caused us to reason out the table on the right of the 225c for Venus, whereby the number 144 also lies at midpoint on that progression as well . One may thus observe a possible reason why the number, 144 is considered to be the number of life itself in many ancient cultures; finding an expression even within the Bible.

Historically significant relationships appear on the above table of numbers. The base measurement of the pyramid of Cheops, 756, appears on the table at the right, directly across from the numbers 1296, an important number cited by Egyptologists (Tompkins). The only number repeated on this section of the table (since it may carried out to infinity in either direction) are: 1656/1656; 144/144; and, 1944/1944.

The number 9 is often cited as significance in conceptions of the Creation. It is necessary to note that many of the numbers have the sum of their integers equal to nine. Consider, for example:

Other numbers on the table have their corresponding integers add to either 18 or 19 in each case; which are also significant numbers in the Mesoamerican reckoning system. For example, they serve as the basis for the multiples of the maya long count in its different levels (Earth/matriX No.1).

The number 144, then, of the maya long count, reveals a direct relation between the 360 day-count of Earth and 225 day-count for Venus's sidereal orbit, in relation to other historically significant numbers (216, 756, 936, 1296, etc.) For such relationships to be a mere result of coincidence would be difficult to sustain.

The numbers appear to be communicating ideas regarding direction, possibly in time and space. Consider the almost perfect relationship that has already been pointed out earlier:

1296 divided by 819	=	1.58241758241...

and,

936 divided by 819	=	1.14285714285...

The numbers definitely indicate direction in terms of numerical progression The number 144 reflects a direction towards the left; the direction that was predominant among ancient Mesoamerican cultures:

144 divided by 819	=	.17582417582...

Again, the basis for pointing out direction has to do with the unit one being divided by the 'perprtual motion' number 7, which produces the 142857 progression.

A possible relationship of the 936 and 1296 fractals may have to do with the Great Sun cycle, theoretically posed as 26,000 years (365c). However, on a 360 day-count, the 936 fractal becomes relevent:

The 1296 fractal may be related, in a like manner, to the lunar 360 day-count employed in antiquity; but, in relation to the time cycle regarding the Great Cycle of 36500 years, identified in ancient Egypt in terms of a computational adjustment: inasmuch as 360 x 36000 = 12,960,000; and 360 x 3600 = 1,296,000. The cycle of 3600 years has also beem cited as historically relevant in terms of biblical time.

It may be impossible to historically situate these numbers as yet. However, the computational logic of their apparent correspondence should serve as a basis for considering their scientific meaning.

Observation

In this essay, we have attempt to explore further the possible logic of number that occur in the historical record of the ancient reckoning system of Mesoamerica. We have attempted to perceive a possible significance of the 819 day-count, which has been related to the K'awil glyph/figure in ancient maya sculpture.

Time and again, the apparently singular nature of some the historically relevant numbers of the maya, would appear to relate in an exact theoretically conceptual manner with other equally peculiar numbers. The numbers are evidently not strange at all; we have simply not discovered their inner logic, their internal workings. By attempting to discern their internal logic, how the different numbers behave with respect to one another, we may come to comprehend their function and meaning, not only in astronomical computations, but in their philosophical meanings. We may be expecting to reconstruct too much as of the numbers themselves, but we have long come to learn that nature itself may be reflected and expressed on many different levels through numbers.

The 819 day-count number associated with the K'awil glyph/figure may be one of those significant keys to just such an understanding of the ancient reckoning system of Mesoamerica, and possibly even of the Egyptian system, inasmuch as they both appear to be related (Earth/matriX No.24) .

Earth/matriX
Science in Ancient Artwork Nº.29
THE HIDDEN NUMBERS OF K'AWIL
10 September 1995
©1995-2012 Copyrighted by Charles William Johnson. All Rights Reserved
Reproduction prohibited without written consent of the author.