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AND SPACETIME/MOVEMENT
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Table of Contents The Maya
Long Count and Spacetime/Movement |
by Charles William Johnson
Introduction
It has often been cited that the ancient cultures were concerned with
counting whole cycles of time regarding the planetary bodies of the
solar system. We have also pointed out in earlier writings that by counting
time, one necessarilly is counting space as well. For reality exists
as spacetime. Furthermore, spacetime is movement. In the essay Earth/matriX
No.37, we pointed out how the maya long count, a 360 day-count
may also be related to the numbers of the Universe that pertain to the
velocity of the Earth, the Sun, and even that of light. That may be
simply a feature of numbers in and as of themselves; that they are relational
among themselves outside of the events being considered. However, there
would be some relationships of coincidence among the numbers that might
cause one to believe that the ancient maya system of the long count
may have actually taken into account the speed of light, which has been
clocked at 186,000 miles per second.
The numbers of the maya, often cited by researchers are notoriously
long. For example, consider the number 35,530,560,000 days, which is
the result of the multiplication: 97,344,000 years times 365 days. Or,
the longest count known of the maya which consists of '260 eras',
where each era is calculated on the basis of 73 Oxlahkatunes:
374,400 years times 365 days: 136,656,000 (Harleston, 1990).
A fractal of this last number has been referred to in the literature
as a companion number (Cfr., Earth/matriX No. 32). The significant
point is not with respect to a particular number, but rather to simply
note how the reckoning of time has been carried out into numbers that
would appear to reflect cycles or amounts of time that essentially are
irrelevant to an individual's lifetime on Earth. The intriguing point
has always been the question of why the maya may have counted
time cycles in such lengthy groupings whose meaning for us on Earth
may not be so obvious at first glance.
Scholars have studied the maya long count exhaustively. And,
our comments are obviously based upon those same efforts; much of our
interpretation hinges upon what others have already commented. However,
we should like to consider the numbers that have been employed for counting
time, and observe how they perform when counting space and movement.
It only follows, that if the maya were counting time events,
those time capsules were a reflection of somethings (space) possibly
in motion (movement). In a certain sense it has been suggested that
they were simply counting the relationships of the planetary bodies
within the solar system, and then not all of those bodies. Interest
especially remained with the relationships of Venus and Earth, alongwith
the Sun and the moon. The opposition of the Earth and Mars (780c) may
have also been counted, where every 780 days Earth passes between the
Sun and Mars (referred to as being opposition).
From a mathematical analysis, we have maintained that the different
calendrical day-counts of the ancient reckoning system of Mesoamerica,
would appear to have been developed and functioned as a single system.
In other words, the day-counts 260c, 360c, 365c, and 584c, alongwith
the 225c, in fact all emanated from a single mathematical model of theoretical
conception, based on astronomical observation of the cosmos.
Such a postulate contradicts the popular ideas that hold that the 260c
and the 360c were, in fact, errors in observation of the ancient astronomers,
which were later corrected to the 365c. Many scholars do not even recognize
the 225c, although some do speak about it (Harleston).
Nonetheless, it would appear, from the math, that all of the day-counts
formed part of a single system of reasoning or time-reckoning. Such
a possibility may become more clear as we consider the numbers in relation
to concepts of space and movement; and not only with respect to time.
Velocities of the Earth, the Sun and Light
Let us look at some of the numbers that pertain to time intervals regarding
the travelling time/speed of the Earth, the Sun, and light. These numbers
may hold a clue to comprehending a possible origin or relationship for
the maya long count and some of the aspects of the ancient reckoning
systems of Mesoamerica.
| Miles travelled in a: | Earth | Sun | Light |
|---|---|---|---|
| Second | .310185185185185... | 2.22222222222222... | 186,000. |
| Minute | 18.6111111111111... | 133.333333333333... | 11,160,000. |
| Hour | 67,000. | 480,000. | 669,6000,000. |
| Day | 1,608,000. | 11,520,000. | 16,070,400,000. |
| Year: | |||
| 260c | 418,080,000. | 2,995,200,000. | 4,178,304,000,000. |
| 360c | 578,880,000. | 4,147,200,000. | 5,785,344,000,000. |
| 365c | 586,920,000. | 4,204,800,000. | 5,865,696,000,000. |
In the previous essay (Earth/matriX No. 37), we demonstrated how the numbers of the preceding chart emanating from the measurement of time regarding the Sun and the speed of light are divisible evenly by the numbers of the maya long count. An obvious relation does exist, but may be exemplified further if we consider the cycle of the Sun, which has been identified by contemporary astronomers as being 250,000,000 years (365c). Let us now observe the numbers that correspond to that particular cycle.
During a single cycle of the Sun within the galaxy, the Milky Way, which takes 250,000,000 years, the corresponding miles travelled by the Earth, the Sun, and light (during that time) are:
| Earth | Sun | Light |
|---|---|---|
| 146,730,000,000,000,000 | 1,051,200,000,000,000,000 | 1,466,424,000,000,000,000,000 |
The Fractal 10512
Within the concept of time-cycles, it could be understandable how a complete cycle of the Sun might enjoy great significance within the ancient reckoning system. Therefore, if that were the case, then the number/fractal 10512 would become extremely relevant for computations. During our analyses of the ancient reckoning systems, time and again the fractal 10512 appeared over and over again. Let us observe how it may perform regading the maya long count numbers and the day-counts as well.
In order to be able to manage the computations, we shall rely upon the system of employing the fractals, keeping in mind the possibility of floating the decimal place in either direction, which appears to have been the procedure followed in ancient times as well.
| 10512 | ||||
|---|---|---|---|---|
10512 divided by |
2304 | = | 4.5625 | |
| 1152 | = | 9.125 | ||
| 576 | = | 18.25 | ||
| 288 | = | 36.5 | ||
| 144 | = | 73 | ||
| 72 | = | 146 | ||
| 36 | = | 292 | ||
| 18 | = | 584 |
From the above divisions, immediate relationships of numbers become obvious. The number of miles travelled by the Sun in a single 250 million-year cycle, when divided by the fractals of the maya long count yield numbers that refer to the 365c and the 584c of the ancient reckoning system of Mesoamerica. In other words, the maya long count may be observed in mathematical relationship to the 365c of Earth and the 584c synodic count of Venus. In a single mathematical exercise divisions and relations are possible among the 360c (maya long count), the 365c and the 584c.
Equally significant from these numbers is the relationship that may be observed regarding the 10512:1152 ratio which yields a 9125 fractal. The number 9125 (days) has often been cited in the literature for a day-count regarding the Sun. It is significant to see that this fractal number (9125) is produced by dividing the total number of miles that the Sun travels in a single day into the total number of miles that is travels in a single 250 million-year cycle.
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By halving the 10512 cycle number, one may observe the fractal 5256. This particular day-count number has been cited by many authors (Lounsbury) regarding the analysis of the companion number 1,366,560 and the tzolkin (260c):
| 1,366,560 | divided by 260 | = | 5256 |
|---|
With that one brings into picture the 260c which is the related to the 10512 fractal in a similar manner in which the other day-counts were related. One begins to get the idea that basically all of the day-counts are related among themselves, and by way of the 10512 fractal, even in such seemingly remote cases as a number such as 1,366,560 of the ancient maya reckoning system.
Now, let us see what happens regarding the 225c sidereal count of Venus. In a previous essay, we have related this particular count to the 360c (Earth/matriX No. 16).
| 10512 | divided by 225 | = | 4672 |
|---|
The product 4672 does not appear to be particularly striking as far as numbers of the ancient reckoning system go. However, let us run it through the doubling/halving method:
| 4672 |
| 149504 74752 37376 18688 |
| 9344 |
| 4672 |
| 2336 1168 584 |
As one now observes, 4672 is a multiple of the 584c (Venus synodic): 8 x 584 = 4672.
It is impossible to offer an analysis of all of the mathematical possibilities of the system. However, it should become clear that the fractals and the numbers allow for assigning them distinct meanings; the same number or fractal there of may enjoy different meanings and reflect distinct time/space reference points or events. The computations may be simply inverted or interchanged. For example, although the 9125 fractal may be found in the historical record as a count of days, it may also represent a mathematical constant, which when multiplied by the maya long count numbers/fractals may refer to the spatial concept of miles travelled by the Sun:
| 91,250,000,000 x 11,520,000 = 1,051,200,000,000,000,000 miles in a 250 million cycle |
The number/fractal 2990 has been referred to in the literature as a day-count for the comparison of the orbits of Earth and Venus:
| 2920 | divided by | 365 | = | 8 | orbits (Earth) |
|---|---|---|---|---|---|
| 2920 | / | 584 | = | 5 | (Venus) |
Yet, at another level of analysis, a distinct meaning may obtain:
| 1,051,200,000,000,000,000 divided by 360c = 2,920,000,000,000,000 |
Or, consider further:
| 1,051,200,000,000,000,000 divided by 365c | = | 2,880,000,000,000,000 |
| 146 | = | 7,200,000,000,000,000 |
| (Egyptian Sothic cycle numbers) | ||
Possibly one of the most interesting relations obtains when we consider the number 13 in relation to the 10512 fractal. How many miles would the Sun travel in 13 cycles of 250 million years? Thirteen times 250 would be 3250 (325c). But, more significantly, consider:
| 13 x 10512 = 136656 fractal of 1,366,560 companion number |
In this manner, one may comprehend how the 260c and the 360c are related, given that 13 is a multiple of both counts; thereby also being relational to the other day-counts of 365c, 584c and even the 225c. At sufficiently large numbers all of the day-counts are relational to the 136656 companion number, which in turn is relational to the space/movement number/fractal: 10512.
The Maya Long Count and the 365c
The maya long count is based on a 360c day-count. However, from the above analysis, it may be seen how the maya long count numbers may function as a translation for the 365c day-count system as well. The long-standing procedure in analyzing the maya long count has been to consider the day-count numbers (7200, 144000, 2880000, etc.) by dividing them by 360. For example, 144,000 days is generally referred to as being or representing 400 years (360c): 144,000/360 = 400.
From the perspective of computational math within a method that may have been followed by the ancient astronomers, and which is suggested in the logic of numbers as we have illustrated lies another procedure, which may not be in the historical record, or which may be there, but we simply do not know how to read the glyphs accordingly as yet. Consider what happens when the maya long count numbers are considered to be multiples or constant numbers for the 365c:
| 365 x 2304 | = | 840960 | divided by 360 | = | 2336 | (584c) |
| 1152 | = | 420480 | = | 1168 | ||
| 576 | = | 210240 | = | 584 | ||
| 288 | = | 105120 | = | 292 | ||
| 144 | = | 5256 | = | 146 | ||
| 72 | = | 2628 | = | 73 | ||
| 36 | = | 1314 | = | 36.5 |
With this chart one may see how the 365c and the 360c numbers become inversely related to one another:
| 365 | : | 360 |
| 360 | : | 36(5) |
On this same chart, the 365c, the 584c, the maya long (360c), and the numbers relating to the Sun's distance travelled in 250 million years are all related easily and evenly.
The system if further relational to the 260c as we have already mentioned:
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Possible relationships are unending, just as the measurement of spacetime/movement within the Universe is itself infinite in nature. One could then bring into consideration other day-counts, such as the k'awil (819c) as we have done in previous essays (Earth/matriX Nos. 29-30), but would make this essay excessively long. In subsequent essays, we hope to further the analysis of possible computation of spacetime/movement in the light of the maya long count and the reckoning system of ancient Mesoamerica.
Observations
From the extreme coincidence of numbers it is possible to consider the fact that the maya long count numbers/fractals represent a system which may have taken into consideration the spatial and relational aspects of time and its measurement. The reckoning system of ancient Mesoamerica would appear to represent a single system of reasoning, supporting the idea that it appears to have been developed at a single stroke. Nonetheless, the system would appear to have employed methods of analysis (duplation/mediatio) which were worked out over thousands of years of human endeavour given its apparent simplicity for managing complex numbers.
From an analysis of the numbers in relation to the concept of time alone, and the idea of time-cycles, it would appear that the purpose of the system was so abstract as to defy any significant meaning. It would appear to have simply assigned meanings of abstracted relations among the planetary bodies, which somehow does not tell us much for that age. However, from the perspective of space (bodies) and movement (distance travelled), the numbers/fractals of the maya long count would appear to take on greater significance something more tangible for us to comprehend. The ancient astronomers were measuring not only the time-cycles of the planetary bodies, but possibly considering and exactly knowing the distance travelled by the planetary bodies throughout the Universe, or at least, within the galaxy that we live in.
The question immediately arises as to how they may have possibly know such events actually occurred within the cosmos. It would be simple to conclude that possibly someone from another part of the Universe offered them this analysis and data. Yet, the manner in which the data appear to have been generated, and the numbers situated within the maya numerical system, appear to be far too elaborate and even clumsy (since we do not really know how the mechanics of the system worked) from the perspective of the glyphs. If they had been given this knowledge by a visiting culture, then surely they would have been offered a more streamlined manner for annotaing the computations, and not the laborious dot-dash system of the maya numerical system. For our computations, we must remember, we have used pocket calculators and a numerical system of annotation that allows for quick reference and speedy computations. What we have been able to discuss in a score of essays in the Earth/matriX series must surely represent thousands, even millions, of computations by hand (or mental abstraction, possibly) over millenia.
It is difficult to conclude, muchless prove, that the matching numbers, the many coincidences in the computations and their infinite possibilities, were actually the way things ocurred. The historical record simply is not there; it has been destroyed; and if the computations existed in mind alone (mentally), then the record was never even made in the first place. If the computations are there in the historical record, and we are unable to read them as the stand, then possibly with time, a new reading of the historical record may come into view. For the time being, the analyses of the logic of numbers may offer insight into how that record may be read in a distinct manner from what has been achieved in the past. We do believe that the recrod has been read correctly, but possibly there may be other relations within the meanings of the glyphs that we have not considered. Since this author does not know how to read the glyphs, then possibly the findings of these analytical considerations regarding the logic of numbers may be helpful to others in their endeavours to understand one of the most intriguing systems of knowledge recorded by humankind: the maya long count and the reckoning system of ancient Mesoamerica.
Earth/matriX
Science in Ancient Artwork Nº.38
THE MAYA LONG COUNT AND SPACETIME/MOVEMENT
3 November 1995
1995-2012 Copyrighted by Charles William
Johnson. All Rights Reserved
Reproduction prohibited without written consent of the author.
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