Introduction

Generally, the conceptualization of time and the cycles corresponding to the day/year-counts and the orbital timing of the planetary bodies is represented as a relationship of circles. The explanations of the ancient Mesoamerican calendars (260c; 360c; 365c) are also illustrated by a series of turning wheels acting as gears. These illustrations arise from the ancients in having used the circle for such calendrical examples themselves as in the Aztec Calendar, which represents a relationship of gear-like rings.

The time cycles and the orbital timings of the astronomical bodies may be illustrated with matrices in a graph-like manner. In fact, as we view this possibility of presentation, it becomes apparent that some of the ancient patterns may have derived from a similar conceptualization. The ancient artwork of many cultures of the Western Hemisphere reflects a strong sense of geometrical figures. Some of these geometrical designs are quite similar to the graph-like structure of the matrices that we shall present below.

We shall present only a few examples to illustrate this relationship between the geometry of design and the time cycles of the ancient reckoning system. Numerous other possibilities become available once we comprehend the geometry a matrix in this manner. However, it is not our purpose to exhaust the theme at this time, but merely to establish this particular view on ancient artwork as another possibility of the theoretical conceptualization of the knowledge of the ancient reckoning. It is difficult to affirm whether or not such a procedure was employed by the ancients. There is no evidence in the historical record. We do know that they employed grid-like structures in their paintings and sculpture at times, but other than that, the method utilized in computing time cycles has been lost to date.

Calendars and the Ancient Reckoning System

The oldest calendar of ancient Mesoamerica is said to be that of the 260 day-count (260c). Then, came the 360 day-count (360c) calendar followed by the 364c and the 365c calendars. This progression of day-counts, becoming ever more accurate with regard to the orbital time of the Earth, suggests a logical historical time-line. Generally, most scholars support such a development in the day-counts. In our research, early on, from comparing these different day-counts, we suggested that possibly the 365c came before the 260c, which would not be very comprehensible from a logical point of view of interpretation. We would rather think that the ancients missed the mark in their day-counts (hence the 260c), and steadly corrected their observations till they finally arrived at the closest count (365c).

In fact, many scholars suggest that the ancients discarded the bothersome fraction of the year-count (365.25c) in favor of simply using the 365c. And, even this was discarded in favor of the more neatly bundled 360c, which obeyed the ancient 60c system. All of these things are affirmed in the face of an historical record that shows that the ancient had a precise and exact knowledge of the orbital timings of the planetary bodies in our solar system, and beyond.

Scholarly interpretation emphasizes a rudimentary day/year count system(s), while at the same time marveling at the exactness of the actual counting (predicting events such as eclipses). Let us simply offer a brief view of the day-counts as they appear related to one another on a simple matrix of the 360c. It is said that the ancients employed the 364c for their mathematical computations. As we shall see, the graphics of the different day-counts, in fact, reflect an interrelationship amongst themselves on many different levels. The case is such that it would appear, even in graph form, that the 260c came about after the 365c was worked out, given its visual relationship to the 360c, 364c and the 365c; along with its relationship to the other astronomical counts of Venus, etc. (225c, 584c, etc.).

Logic would have it that we might believe the progressive development of a reckoning system to have taken thousands of years, based on empirical astronomical observation. And, the evidence of trial and error should be itself evident in the logical flow of numbers, going from erroneous counts (260c, 360c) to correct counts (365c; 365.25c). The possibility of having achieved a correct count (365c), and then, having devised an apparently erroneous day-count (260c) would seem to make little sense to us latecomers.

Let us see what the graphic nature of the matrix might communicate to us.

A Rendering of Time on a Matrix/Graph

The 260c calendar is generally divided into a relationship of 13 (time periods) x 20 (days). This 260c count reflected the twenty days in relationship to 13 numbers; thereby, existing more days than numbers, the graph appears as follows:

In reading the matrix from left to right, the black squares represent the initial series of the 20c on the 13c side of the matrix.

Now, let us expand the matrix to accommodate the 360c, which consisted of 18 months and the same 20-day count. In the following matrix, we have the twenty day-glyphs running to the right, and the eighteen months running downward. Now, within this matrix, we need to chart the pattern of the 260c, meaning the combination of the twenty days and the corresponding thirteen numbers. The 13c, in fact, reflects the 13 deities of the days. In this counting procedure, the days were assured of receiving the protection from each one of the thirteen deities at some point in time. It is said that a complete cycle, known as a calendar round, whereby the same day-glyph, deity, time period would repeat itself, took 52 years, or 18980 days.

Now, let us place some of the elements upon this matrix, such as the 260th day; the 360th day, the 365th day, and the initial day of each thirteen-day period within the day-glyph count.

The final five days of the count were considered to be unlucky days. Nonetheless, the ancient reckoning systems appear to have employed all of the counts for their reckoning purposes. One can readily comprehend such a computational relationship since the 260c represents a fractal expression (multiple) of the 13c (2 x 13). Hence, the computations based on the 260c, 360c, 364c, and 365c, might appear to be mathematically unrelated, whereas they were all relational in computational math, and the kind of remainder mathematics that the ancients apparently employed. These relationships in math have been discussed in earlier essays of the Earth/matriX series, and it is beyond the scope of this essay to enter into a detailed illustration of these ideas.

The previous illustration reveals a definite pattern, which has already been observed by others (Cfr., Raúl Noriega, La piedra del sol). We shall expand upon the nature of this basic pattern, and illustrate how possibly ancient designs may have come from this essential matrix.

Notice where the 260c day falls within this 365c calendar. It is well known that the natural emblem of Mexico's Independence from Spain, for example, consists of an eagle and a serpent on a cactus plant, in honor of one of the ancient Aztec legends. Another of its Independence symbols is also based on the ancient 260c Aztec calendar. The national day of Mexico's Independence was declared on the 15th of September, El grito, which falls in some years on the 260th day of the 365c calendar.

Other than that symbolism, the apparent placement of the 260c on the 360/365c calendars would appear to have no relevancy. It would easy to surmise, as most scholars, that these calendars have no relationship among themselves in terms of design. Nonetheless, there is a definite pattern issuing forth from all of these relationships in the previous illustration. Notice the following placement of the 260c as of the relationship of the 20 days and the 13 numbers (deities) within the 360c/365c calendar. It becomes obvious that the 260c day could have been chosen as a conscious design in relationship to its pattern as placed within the 360/365 count calendar.

For, as we saw earlier, there is no apparent design issuing from the 260c by itself, other than a progressive ordering of the black squares, as observed in the fretwork of ancient architecture. However, the 260c pattern (13:20) within the 360c (18:20), now reveals a placement of the final 260 day in such a manner as to be drawing attention to the repeat pattern within the relationship of these calendars. It were as though the 260c day was chosen given its placement in relation to this apparent and obvious pattern as may be illustrated in the following matrix layout.

The pattern established repeats itself throughout for the following year counts. The 260c day, illustrated by the open block square () falls precisely at the end/initiation of the perceived pattern.

It is difficult to think that such a visible relationship of distinction could exist among the different day-counts and not have been conceived as of a conscious choice of the 260c itself. As we have been exploring the possibility of the ancient Egyptian hieroglyphs with the ancient Mesoamerican systems, the pattern disclosed here even reflects one of the ancient hieroglyphs from kemit. The hieroglyph [ ] represents the concept of boundary or limit. The pattern obviously establishes that concept.

Now, let us examine the pattern as of the four years of the 365c.

Key:		=	Day One for the Corresponding Year
		=	The 260th day (260c)
		=	Days 361 - 364
		=	Day 365

The apparent movement of the last five days of the year (361-365) shows a definite step-like pattern on the four-year matrix, which repeats itself. This step-like pattern reminds us of the glyph for the ball game in ancient Mesoamerica, which resembles the step-like pyramids of the area. The last day of the four-year cycle is number 1460 (4 x 365). The fractional expression of the Earth's orbital time is adjusted by adding one day to the calendar; the year is known today as leap year. That would be day number 1461. (It is significant to remember the ancient Sothic cycle, which considered the 1460:1461 cycle, but in yearly terms.)

The Patterns of the Orbital Times of Venus

The planet Venus was extremely important in ancient Mesoamerican thought, being conceived of as the Morning and Evening Star, personified in Quetzalcoatl and Xolotl. We shall present the sidereal orbital time (225c) and the synodic orbital time (584c), as they were apparently employed in the ancient reckoning systems of various cultures.

As one may observe from the pattern established, a direct relationship could be drawn with other geometrical patterns found in much of the ancient artwork in many different cultures. In fact, depending upon how one observes the graphic relationships, one could devise distinct patterns based on these numbers.

As can be seen in the previous illustration, the sidereal pattern of Venus repeats itself. There are different ways to visualize the pattern. We have chosen one that reminds us of many ancient geometrical patterns found on pottery and other wares. For example, we may visualize it as follows:

The sidereal pattern produced by the 584c of Venus produces the same pattern, only it is more elongated.

Observations

The patterns that have been illustrated above may serve as the basis for creating many different kinds of visual effects. Upon viewing the distinct patterns one is reminded of the fret work adorning much of the ancient Mesoamerican artwork. If the fret work (las grecas) are representations of the orbital timings of the planetary bodies, then we may consider a scientific basis to the artwork itself.

The patterns repeat themselves at different intervals. The 365c day-count repeats every four years; the 260c repeats itself within the 360c day-count; the 225c of the sidereal count of Venus repeats every 2+ years; the 584c repeats its pattern every 8 years; the 360c has no pattern, for it serves as the basic matrix for all the other patterns.

These patterns are quite similar to the way in which the phases of the moon, for example, are illustrated on contemporary posters. For example, there are posters that show the phases of the moon for a century, and they are similar to this kind of geometrically structured pattern of the 260c on the 360c matrix.

From the pattern given by the 260c calendar within the 360c calendar matrix and the 365c, we can see how the possibility exists that the 260c was chosen as of its relationship to the pattern fixed on these other calendars. The case could be made to show that the 260c was a conscious choice for many reasons; one being, that of computational math and the precession cycle of the Earth.

Let us remind ourselves of some of the math that we have been dealing with in the Earth/matriX series. Consider the following simple example:

	52	x	365	=	18980 days (the calendar round)
	73	x	260	=	18980 days
Now,	52	x	260	=	13520
	18980	-	13520	=	5460 2730 1365

Now, if we do some reverse engineering, and if 1365 is considered to be 1366.56 (the maya companion number), then:

	1366.56
	2733.12
	5466.24	-	18980	=	13513.76

Now, 13513.76 / 260 = 51.976
25.988 (a nice fractal number for the precession). And, furthermore, 1366560 - 1351376 = 15184 (a fractal number of an historically significant number of the ancient reckoning system: 151840). Remember, 151840 x 9 = 1366560 (the maya companion number).

The numbers of the ancient reckoning system flow from and into one another with great ease. They give the impression of having been created as a single system, as we have been illustrating in many different essays and extracts.

©1999-2012 Copyrighted by Charles William Johnson. All rights reserved.