Earth/matriX
SCIENCE IN ANCIENT ARTWORK

Extract No.18

# The Platonic Year & the Maya Long Count: Fractal

By

### Charles William Johnson

In reviewing the ancient reckoning systems, one can only wonder to what extent the historically significant numbers obey the laws of mathematics, and to what extent they were consciously chosen by the ancient themselves. As we have seen throughout the Earth/matriX series of essays and extracts, the ancient reckoning systems appear to share a common logic of computation. One of the most historically significant numbers concerns that of the Platonic Year (or Platonic Cycle), which reflects the 25920 years of the precession of the equinoxes (often cited as closer to 26000 years of Earth's orbital timing). Most scholars do not recognize the possibility that the ancients conceived, much less knew, the timing related to the precession of our planet around the sun. We have seen how the number 25920 (and fractals thereof) may have been derived from different points of computation; simply by doubling 810 (1620, 3240, 6480, 12960, 25920), one may easily arrive at this figure.

Yet, the fact that the precession itself seems to be such a complex idea, the rotation and revolution of our planet around the sun, drawing an imaginary, circular-like axis with its own axis, somehow suggests a much more complicated computation for deriving the Platonic Year. In fact, it would appear that we would not expect nor suspect that the ancient maya reckoning system, the maya long count, based on the numbers/fractals 360, 7200, 144000, 2880000, 57600000, 1152000000, 23040000000, might be relational to the Platonic Year at their face value. In ancient Egypt (kemi), an historically significant number has been cited, which is 1296000, and is evidently half the fractal value of 2592 (1296 x 2 = 2592). But, the maya numbers/fractals are not that evident, since the known academic literature does not explore the relations that we shall examine herein.

Before we examine the relationship of the Platonic Year to the maya long count system, we should point out that the relationships illustrated in this extract employ a way of viewing the numbers that is not readily accepted by the academic community. The very concept of "fractals" is not one that is so recognized; nor is the idea of the ancient reckoning system as having employed a "floating decimal place", one that is to be found widespread throughout the literature. Yet, from our studies, we have come to recognize the possibility that the ancient reckoning systems may have used these different methods for their computations. This would mean that some well-accepted ideas today are in fact erroneous. For, by using the concepts of fractals, floating decimal places, and relational meanings to the same number (whereby a single number may mean different cycles of time), we see the system come alive.

One way to imagine the concept of fractals and that of a floating decimal place is to precisely move the numbers/fractals of the maya long count in relation to themselves, whereby we see appear numerous historically significant numbers coming out of the addition thereof. In fact, one may immediately derive the Platonic Year of 2592(0000000) from two specific cycles:

 2304 0000000 alautun 288 0000 pictun 2592 Platonic Year fractal (25920)

Were this the only historically significant number/fractal to come out of such a strange way of visualizing the maya long count numbers/fractals, we might attribute this to mere coincidence. However, as we have been examining throughout our research, the coincidences are far too numerous to believe that the ancient maya chose their particular series of numbers, in relation to the 1,2,4,8,16,32,64,128,256,512,1024,etc., constant series of numbers out of a lack of understanding of mathematics. Quite the opposite; the number series reflects a profound knowledge of mathematics, and geometry as we have illustrated previously in other essays.

The common thesis posited by most academics is that the ancient maya avoided the fractions. As we have stated herein; if they avoided the fractions, then that means they knew the fractions. Knowing them is the only way to avoid them. But, possibly they did not only know our present day concept of fractions; they possibly conceived of numbers in a much more dynamic manner as fractions, fractals, and floating decimal places; as illustrated in the previous example ---for which we have no particular vocabulary to express.

Academics today are still not certain about the specific meaning of any particular number coming out of the ancient reckoning system of the maya or the kemi. For example, one may read all of the debates around the number of the k'awil (819c); the companion numbers (1366560 and 1385540); the day-counts themselves (260c; 360c; 364c; 365c; 580c; 584c; etc.); 31104; 151840; etc., there are far too many numbers to review here. Yet, what is a given fact is the manner in which one may derive almost any of these numbers (and then some) from the simple addition of the maya long count numbers/fractals themselves.

Let us examine a few of these historically significant numbers/fractals as of the maya long count system. If one were not certain that the previous illustration may be possible in order to derive the 2592 fractal; then, consider other combinations (again we can only show a few; the options are infinite):

 2304 0000000 2880 000 5184 5184 / 2 = 2592

If we missed it one way; then, we may visualize it another. Another historically significant number appears from these same numbers, arranged differently:

 2304 0000000 28800 00 31104

The 31104c fractal has been cited as significant to ancient Teotihuacan and ancient China, as well. A number such as 31104 represents an apparently conscious choice; not a number that occurs naturally in any of the methods that we may concern ourselves with in mathematics. One would have to double 243 (486, 972, 1944, 3888, 7776, 15552, 31104) or, triple 128 (384, 1152, 3456, 10368, 31104) in order to derive this particular number. With that, we see other historically significant numbers appear on these two series.

Numerable other historically significant numbers become available when we employ this procedure throughout the maya long count numbers/fractals:

 360 360 360 360 360 360 360 7200 144000 2880000 1152000000 23040000000 396 756 18 648 1512 2340

A complete table of combinations must be drawn up in order to observe the wealth of historically numbers that may be produced by this simple method. The numbers/fractals may also be relational as of multiplication and division; not only addition of their face values.

 360 x 1.44 = 518.4 360 x 2304 = 829440 364 x 2304 = 838656 414720 419328 207360 ... 103680 3278 51840 1638 25920 819 (k'awil)

 Or, consider, 1366560 / 2.304 = 593125 1186250 2372500 4745000 9490000 (= 26000 x 365 the number of days in the precession without the fractional expression of the day-count 365.25).

In this example, we see two historically related numbers (1366560 and 2304) as a function of the precession day-count. Inversely, the maya long count fractal/fractional expression, 2.304 times the 9490000 day-count yields the maya companion number:

 2.304 x 9490000 = 21864960 10932480 5466240 2733120 1366560

We know that the fraction/fractal 625 is significant in the ancient reckoning system. One might consider a single example: 360 / 576 = .625, in order to comprehend this relation in the maya long count. In previous studies, we have reviewed the .625 and .225 relations as of the sidereal orbital timing of Earth and Venus (Cfr., Earth/matriX No. 16). Consider some peculiar relationships:

 1366560 x .225 = 307476 576 x .625 = 360 614952 720 1229904 1440 - 1366560 2880 1366560 5760

The constant series number (64c) reveals some interesting relations as well:

 576 x .64 = 368.64 Now, Consider, 368. 64 184.32 - 365 92.16 3. 64 (that is the 364c) 46.08 23.04 368. 4 11.52 - 360 8. 64 (= 432 x 2; the Consecration number)

The decimal floats obviously. With that, historically significant numbers/fractals appear on demand, and unsuspectingly. The numbers/fractals of the maya long count do not appear to have had only one singular meaning; the manner in which they relate to other historically significant numbers suggests a much more complex system of computation. The numerous historically significant numbers, cited in the texts of ancient history, and the maya long count numbers/fractals, appear to form a very compact system of computational possibilities. Furthermore, these possibilities overflow into the system of ancient reckoning that was present in ancient kemi, given the fact that similar computations become available in a very similar manner. Almost all of the historically significant numbers/fractals appear to be related and share a common origin; one that is not totally natural to the manner in which numbers perform and relate to one another. But, rather, these relationships appear to have been based on conscious choices and design.

The number related to the precession of the equinoxes, as we have discussed in this extract, may be derived in a natural manner, but it may also come forth from the very numbers/fractals related to the maya long count. Even that fact somehow represents a coincidence that defies explanation. The cultures of ancient Greece and Europe may have chosen the number 25920 simply because it had already been chosen by design centuries or millennia prior to them. The ancient maya long count enshrouds in an inherent manner, through simple addition, the very numbers that later came to be known as the Platonic Year. It may, then, simply be the other way around; the way history would have it. Firstly, the ancient cultures of Mesoamerica and Egypt discerned the precession, identifying it as 25920 years; and, then, secondly, the later cultures built upon that discovery. A timeline would have it no other way in fact.

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Reproduction prohibited without written consent of the author.

Earth/matriX
Science in Ancient Artwork
Extract Nș.18
The Platonic Year & the Maya Long Count: Fractal
July 14, 1997