Now that we have seen how the maya long count numbers (360c) perform regarding the numbers of events such as the velocities of the Earth, the Sun, and light, some considerations are in order concerning measurement (numbers and proportion), and the measurement of spacetime/movement coordinates and events. Much of the comparative work that we have been presenting in the Earth/matriX series revolves around the coincidence of numbers and proportions. For that reason such studies may be viewed as simply numerological in essence. In fact, any identification of numbers and proportions is somehow discarded by many scholars as simply constituting a play of numbers. Nothing could be farther from the facts, inasmuch as it is possible to assign numbers to spacetime events, as the ancient astronomers knew so well. For that reason we have chosen the path of examining the internal logic of the assigned numbers, in an attempt to comprehend what they reflect and possibly, although this is more difficult, why were they chosen.

The kinds of reasons that may have been present in assigning meanings to numbers and proportions (designs in geometry, for example), may have been infinite, and we may never come to know those reasons with any degree of certainty. If we understand these innate limitations to our study of the past and the ancient artwork, then we may possibly become more relaxed about any particular coincidence of numbers or proportion pointed out in these studies. We can never emphasize enough, that there is no effort on our part to state that a particular relationship is the one that explains everything or actually constitutes what may have occurred thousands of yeras ago. Such determination and exactness of defending particular interpretations of past events would seem opposed to the very uncertainty of the historical record itself which has been simply reconstructed piece by piece, never hoping to find a comprehensibly written tract that might offer all of the answers to the questions that we raise.

For example, the system of numbers of the ancient reckoning of time by the peoples of Mesoamerica would appear to be extremely difficult to manipulate by way of the dots and bars of the maya system. We do not really know how they did; possibly we are only observing the results of their analysis in such documents as the Dresden codex. The actual computations seem tobe no where around, although it would appear that scholars of things maya have accurately interpreted much of that record and those procedures to certain extent. All of that leads this author to consider the possibility that the ancient maya effected the computations mentally, in their heads. There was no need for annotation because everything was accomplished mentally, abstractly.

Inspite of all of the facts that somehow stare us down in the historical record, we continue to attribute errors to the ancient reckoning systems' essential measurements. The 360c systems of ancient Egypt, and the 260c and 360c system of ancient Mesoamerica, nonetheless, are often considered to be nothing short of simple errors in measuring time by those ancient cultures. As we have attempted to illustrate in the Earth/matriX series, nothing farther from the facts may be present than such a conclusion. The 260c and the 360c not only reflect a mathematical logic of numbers, but also reflect spacetime coordinates of the events counted, the astronomical events of the solar system and the Universe. Such a coincidence of numbers and proportions of spacetime coordinates would be difficult to set aside were it not for the fact that we somehow have never really come to grips with the idea of numbers, of measuring spacetime itself. Even today, contemporary physics grapples with just such a problem of knowing how to measure through a coincidence of numbers and proprtion spacetime/movement events that are in fact already existing as such: spatially, temporally and relationally interconnected.

The question arises then as to whether the ancient peoples were able to have achieved something that we have yet to accomplish. It would appear that the logic of their numbering system and their system for reckoning time may reflect a conceptual knowledge of how to measure spacetime at distinct levels, translating coordinates from one level to another with the same ease with which those events exist. Let us explore the logic of numbers a little further in our search for an understanding of the scientific basis in ancient artwork.

Numbers and Proportion in Measurement

Spacetime can be quantified, counted, and the natural order of spacetime/movement itself determines the logic of numbers (the quantification of events). The existence of spacetime/movement determines, in a sense, what occurs first, second, third, etc.; that is the mechanics of spacetime itself. At certain levels of existence that order would appear to be contradictory, as expressed in Newtonian physics and the physics of relativity. Albert Einstein had the suspicion that there was essentially no contradiction and that it was possible to achieve a theoretical conception of what has come to be known as or referred to as the 'theory of everything', or previously as the 'unified field theory'. Whatever the name, it would apper that the theoretical conception and expression of existence itself, spacetime/movement, can be enunciated in a single set of terms; just as reality itself exists in a singular manner as spacetime. The names vary; the events remain the same. Every day we appear to be a little closer in identifying and expressing the terms of existence itself.

Throughout history different systems of measurement have come into existence regarding the human concern for measuring things. In fact, the ancient reckoning systems is just such a system of measurement. Today, we have two main system of weights and measurements. For now we are concerned with the side of measurement only. The English (British/American) system based on yards/feet/inches, and the French system based on the meter/centimeter/millimeter. The conversion of one system of measurements to the other constitutes a virtual headache for almost anyone, and a real bother when the wrench for the car bolt is in the wrong system. Yet, in terms of numbers, it would appear that the similarities between the two system were not as drastically bothersome. In fact, as we have seen when we compared the numbers of the ancient maya long count system with the distances in miles of the planetary bodies of the solar system, alongwith their velocities, then the coincidence of numbers was quite startling.

In comparing the ancient reckoning system with the metric or English system, different scholars prefer one or the other. And, somehow the measurements always produce coincidences. Other authors (Harleston, 1990) have attempted to discern the actual unit measurement of the ancient system of Mesoamerica, identifying a Standard Teotihuacan Unit (1.0594 meters), which converts the metric system numbers into numbers that reflect the maya long count numbers (and multiples). Yet, when another author (Munck, 1993) analyzes the numbers of the ancient Egyptian system in terms of the English system, the numbers also check in terms of coincidences. One would naturally conclude that something is wrong, or that that is the way numbers perform. That is why much of these studies are sometimes discarded or ignored by many scholars, because simply the numbers cannot check in all of these different systems. But, they do, and the logic of findings by many of these authors should be considered more profoundly because knowledge is to be gained from the comparisons and the coincidences of numbers and proportions.

It is not uncommon to read disqualifying remarks that those 'numerological' studies mean nothing, that it is a simple case of proportions. Such positions do not seem to realize that proportion is the reflection of anumerical progression, wich involves the laws of geometry, for example, which reflect the laws of nature; i.e., the coordinates of spacetime. This has become much clearer at present in the study of fractals which work so well in the visuals of contemporary computers. The fractal numbers appear to reflect the proportions of growth in nature. Those same procedures appear to have been the basis of reasoning in the ancient reckoning systems, whereby the whole cycle of numerical progressions (day-counts) can be charted into visuals of fractal images, much like the graduated image of a leaf.

The logic of numbers of the ancient reckoning system would appear to be designed and consciously based upon the notion of fractal numbers (the progression of numbers) and their expression in geometry. Just as fractal are today a concept of science, so it was for the ancient astronomers and mathematicians, who consciously designed their own systems of reckoning time and space and movement. By choosing specific progressions of numbers for their designs, particular repeat patterns would occur in the artwork. The laws of geometry are visible in the artwork because the logic of numbers lies therein, which in turn reflects a conscious measurement of the spacetime coordinates.

The Numbers of Measurement and Spacetime

Let us review a few example which might explain partially how different analyses based on distinct measuring systems may be comparable and reveal underlying relations of coincidence. One example that comes to mind inmediately is that of the Great Pyramid of Khufu. We have discussed some of the numbers/measurements pertaining to this ancient work of art in earlier essays (cfr., especially, Earth/matriX Nº.29, 30 and 33). The linear base measurement to the Great Pyramid of Khufu has always been under debate as to its exact number. But, let us deal with the commonly cited numbers of 756 feet and 216 meters, which are quite approximate to the base measurement of the Sun pyramid of Teotihuacan measured extensively by Hugh Harleston. To observe these two systems of measurement expressed as such, there would appear to be no apparent way to compare them; in fact, authors generally keep to one system of measurement in order not to confuse readers.

The number 756 does not divide a evenly by 216:

So, these systems of measurement would appear to be unrelated or impossible to relate Obviously that is not the case; one simply doubles the 756 number and an even number of divisions is produced although in an odd integer:

Now, the systems may be easily related. There are many interesting points that we shall not be able to mention as they lie without the subject at hand, but the fact that one system of measurement emphasizes a number (756) that is relational to other numbers (819) of the reckoning system of ancient Mesoamerica, while the other system of metrical annotation (216) reflects a fractal of the diameter of the Moon's measurement are not unrelated to further analyses of spacetime events registered by the ancient cultures of Egypt and Mesoamerica.

To some, such coincidences of measurement are intriguing; to others, they simply represent how numbers behave among themselves with little to offer in the way of knowledge. Yet, the precision with which the ancient sites and artwork are laid out and designed and executed would reflect that same precision in numerical measurement. The ancient artwork is precise because the knowledge that led to its construction was equally as precise, or even moreso, since theoretically one may design the ´true' pyramid, while in engineering terms it may be difficult to achieve in exactness. Stonework around the world from ancient cultures reflect just such a preciseness to lesser or greater degrees. That cannot be ignored without discarding some of to original purpose of the builders and designers of those systems.

The metric system is apparently based on a theoretical design of 10 units, which is subdivided into halves of 5 units each, infinitely so. The English system is apparently based on the system of 12 units (inches), divided by halves that contain 4 units each, infinitely progressive through 8ths, 16ths, 32nds, 64ths, etc. The systems seem to be extremely unrelated in numerical terms alone, aside from the considerations of actual length. Although it is obvious that the meter could be of the length of the yard with the corresponding adjustments of its divisions/subdivisions, or viceversa, the yard could be altered to the length of the meter with its subsequent adjustments of divisions/subdivisions. In other words, the actual length of a mile could be a kilometer, or viceversa, a kilometer could be brought up to the length of a mile without any problem; spacetime can be assigned and reassigned meanings without any problem.

The key for analysis comes from the ratios of the basic units of measurement; their quantification and numerical relationships. In the end, it does not matter how long the actual event is that is being measured, but how the numbers relate to one another. Consider once more the Great Pyramid of Khufu's numbers:

Impossible one might say, and there would be an example of comparing things that are not comparable. But, actually the comparison is valid in terms of the concepts that appear to have been the basis for the ancient reckoning system. From one perspective actual lengths are being compared in a contradictory manner (inches:meters), but from another perspective measuring units (numerical annotation and abstraction) are being compared.

Ratios : Relations of Difference and Sameness

An essential ratio between the two main measuring system of today (the English and the metric systems) is that of 5:8. The numbers corresponding to such a ratio have already been examined in Earth/matriX Nº.19. At specific intervals the whole numbers are relatable and divisible between the two systems, very much like the comparison that may be made between the orbital times of Venus and Earth:

The 5:8 (or 8:5) ratio reflects the proportional timing between Earth and Venus, which is in percentage terms .625 and has been explained in earlier essays, Earth/matriX Nº.16). That same proportion, .625, is maintained in the 5:8 ratio between the metric (5) and the English (8) systems of measurement. The spatial divisions/subdivisions produce just such a ratio, and may be grouped in different manners of proportion and distinction.

The metric system is based apparently on the unit of 10, or 1.0 meter. Yet, the number ten is a multiple of 5. One may conceive and present the metric ruler/system as 10 theoretically and express it as such, but the ultimate unit of measurement is five (and its multiples).

The English system is based apparently on the basic unit of 12 (inches) allowing for the yard (3 x 12 inches). Yet, that is the theoretical expression. The basic unit of measurement is 8 (8ths of an inch). The fact that the numbers may be multiplied/divided allow for the ratios to vary with respect to one another. Therefore, there are essentially different ways to conceive of these systems.

Their basic ratios may be expressed as:

inasmuch as the number 5 is not evenly divisible into a whole number. Nonetheless, in terms of numerical progression, other ratios exist as alternative conceptions: the two systems may be related proportionally by the ratios of:

The possibilities are obviously unending as far as multiplication and division are concerned in measurements. That is the characteristic of measurement, obtaining comparative proportions of the spacetime coordinates of distinct events. The first act of measurement is the ruler itself, the divisions/subdivisions of spatial coordinates therein.

The maya long count system (360c) is itself a system based on the numbers 20 x 18 = 360, which would allow for proportional progressions of numbers as follows:

Again, the alternatives are infinite. In a certain sense, then, the two essential measuring systems of today are divided along a ratio that counterposes odd (5) numbers to even numbers (8), but which at certain levels become relational in terms of multiplication and division because of the size of the numbers. In a sense, then, all systems of measurement are relational, irrespective of their specific lengths of spacetime coordinates, at the level of the abstraction of numbers. For that reason alone it is easy to understand why many scholars shy away from the study of numbers, no matter how 'scientifically' based the studies may appear to be.

The ancient astronomers and mathematicians were evidently confronted with the same problem: same spacetime coordinates, same problems of the measurement of spacetime.

9125

Let us examine another numerical case which might clarify some of the possible relational aspects of the study of numbers and spacetime. The day-count 9125 has been referred to in the literature (West) as representing a count of days for 309 lunations:

It is pointed out that 9125 essentially represents the multiplication procedure of 25 x 365 (= 9125). That refers to the 25-year cycle of ancient Egypt and the 365 day-count calendar that was also in use then, alongwith the other 360c calendar. Attention is drawn to the fact that it could not have been a question of mere coincidence that a 25-year cycle was chosen in ancient Egypt for the day-counts. The numerical coincidences are too many, inasmuch as the 29.530744365 number is extremely close to the contemporary number for the moon's synodic cycle.

But, such coincidences of number do not only pertain to the comparative analysis of calendrical systems or to lunations. The numbers appear in extremely coincidental terms at other levels as we have seen in previous analyses (Earth/matriX Nº.38). The constant 9125 occurs at other levels of computation for the spacetime coordinates of events in the solar system and in the Universe. Consider the following:

The Sun travels at 480,000 miles/hour. In one day it covers 11,520,000 miles; and, during its 250,000,000 year circuit around the galaxy it covers a phenomenal 1,051,200,000,000,000,000, miles. The Earth travels at 67,000 mph and covers 1,608,000 miles/day and 146,730,000,000,000,000 miles in 250,000,000 years (365c). Light travels ar approximately 186,000 mph and covers 16,070,400,000 miles in a single day and 1,466,424,000,000,000,000,000 miles in 250 million years.

Now, consider the following:

Inasmuch as 9125 represents 365 x 25, then one can understand the following procedure occurring:

For example, the Sun's numbers

A fractal of 250,000,000 years is 25; therefore, 365 x 25 = 9125, the same constant number as in the previous example of lunations.

There would appear to be a conspiracy of numbers not only in the different calendarical system, but in the spacetime events themselves. Significant numbers of the ancient reckoning system not only reflect then the time cycles of astronomical events, but also concur with the distances travelled by those events. It is striking to see that the Sun cover 11,520,000 miles/day, which just happens to be a significant maya long count fractal. Even more significant is the fact that the maya chose the twentieth day to represent a month on their calendar, and the Sun just happens to travel 230,400,000 miles in 20 days; 2304 being another significant fractal maya number (obviously double 1152).

That is a lot of coincidences. The numerical progression chosen by the maya for their long count system (360c) just happens to reflect a similar progression found in the spacetime events of the solar system and the Universe, not only with respect to spacetime as such, but with regard to movement (velocities). The coincidences appear in the astronomical data, in the mathematical reasoning and in the laws of geometry as we have seen in the analysis of the Aztec Calendar for example in previous essays (Earth/matriX Nº 13 & 14). To continue to sustain that the 260 and the 360 calendars were made in error, is to consider the entire system to be an elaborate structure of errors.

The coincidences appear to be due to design, to conscious choice of reasoning, especially when considering other day-count such as the k'awil with an obscure 819-day count, or the companion number 1,366,560. The fact that particular numbers were assigned distinct meanings would not appear to have been due to error in computation, nor to the simple logistics of numbers by themselves, but rather that the numbers are reflecting the measurement of spacetime/movement as it exists, as we also know it.

Observations

In the study of the ancient artwork it is significant to distinguish between the coincidences of measurement and number that may be due to happenstance and those that may be due to human design, a conscious act of knowledge. The ancient artwork would appear to have in part a scientific basis, which is the translation of the sapcetime/movement coordinates into pictorial images and symbols. The historical record, recorded in the artwork, if read backwards towards its internal logic, may disclose to what degree they were able to effect their measuring and theoretical conception of reality. For that we must distinguish the different levels of what pertains to the realm of numbers, mathematics, geometry, and what concerns the assigning of those numbers and measurements to spacetime. The fact that we do not fully understand the meanings that were assigned in a very purposeful manner should not carry us to conclude that the artwork was meaningless.

It is understandable that the numbers would appear to have a life of their own, whereby, in fact, they would sometimes appear to contradict reality itself. And, inasmuch as certain levels of spacetime defy quantification (the concept of movement comes to mind) or challenge its succesful measurement, then the numbers would appear to have limitations of their own. All that obtains because spacetime itself is a constant challenge to be desciphered. Not too long ago scientists still talked about the 'fixed' stars, such as the Sun, as though it were not only stable, but even stationary in space. No one speaks in those terms anymore, and that occurred in our lifetime. Then, we heard that the Sun was on a path, that it had its own 'lifeline' or 'time line'. Then, we found out that the Sun was also revolving within the galaxy, and the line became a curve, only to find out that it was really a spiral, not a line or curve, but a curved, spiraling line.

Obviously, the galaxy must have its own curved, spiraling line as well, rotating and revolving throughout spacetime, moving. Given that spacetime appears to exist in progressions of relations, fractal expressions, it might not be too difficult to think that the numerical progressions alone might suggest certain possible answers to comprehending the next level of spacetime existence. The parts that are known about the ancient reckoning system would appear to reflect at least a sectional view of some of those numbers, some of those spacetime coordinates. Again, the ancient reckoning system of ancient Mesoamerica and ancient Egypt are far too elaborate and precise to belive that they are elaborate systems of error.