Earth/matriX
Science in Ancient Artwork



The Integer (20) Calendar Reckoning and
Astronomical Tables: Ancient Mexico

Charles William Johnson


Part II

The 260 Day-Count

Over the millennia, much of ancient knowledge has been destroyed, both voluntarily and involuntarily through conquest. It is impossible to know exactly how much was destroyed. We may attempt, however, a recreation of the numerical tables that were understandably employed in calendar reckonings of ancient times. The Table of Numbers that we have discussed here might suggest the existence at one time of other tables of reckoning.

We have reviewed the counting system based on the integer twenty method, and the the multiplication of 18 x 20, which offers a pattern based on the cut-off point 360. The 360c has been related to the calendar round of 360 days, with the necessary remaining five days being added on (in maya the name for these five days is the uayeb; in nahuatl, it was nemonetemi).

But, there was an older calendar based on the 13 x 20 relation, producing the 260-day count (260c). This calendar of 13 months and twenty days existed within various cultures of Mexico. "We know that this 260-day cycle count of the days, called the tzolkin by the maya and tonalpohualli by the aztecs, lay at the core of all Mesoamerican calendars, at least since the sixth century B.C. This cycle rose to prominence, I think, because it approximated the length of several fundamental life-sustaining periods: It was a measure of the duration of the agricultural season, nine lunar months (266 days), as well as the Venus appearance interval ..., and it was equal to 13 x 20, both sacred numbers." (from Aveni, p.79).

We shall now consider what might have been the manner for reckoning the 260c in the light of the Table of Numbers (360c) presented in Part I.

We proceeded to follow the same logic of the integer 20 system as in the 18 x 20 (= 360c) calendar round, and devised the following 260c Table of Numbers:

The 260-count calendar round: The old calendar astronomical
Mars Mars Mars
104000 208000 312000 416000 520000 624000 728000 832000 936000 1040000
5200 10400 15600 20800 26000 31200 36400 41600 46800 52000
260 520 780 1040 1300 1560 1820 2080 2340 2600
20 40 60 80 100 120 140 160 180 200
1 2 3 4 5 6 7 8 9 10

Mars Mars Mars
1144000 1248000 1352000 1456000 1560000 1664000 1768000 1872000 1976000 2080000
57200 62400 67600 72800 78000 83200 88400 93600 98800 104000
2860 3120 3380 3640 3900 4160 4420 4680 4940 5200
220 240 260 280 300 320 340 360 380 400
11 12 13 14 15 16 17 18 19 20


In order to produce this table of number based on the 260c, there was again no need to effect a single multiplication. The procedure that we exemplified for calculating the numbers as shown earlier was employed.

Now, instead of using the number 360 as the cut-off point, the number 260 is used. It is significant to note that the numbers related to the 52 and 104 cycles, so important in ancient reckoning in Mexico, appear on the 260c Table of Numbers, although they do so in multiples. Remember that these numbers do not appear on the table of numbers of the 360c. The fact that the cycles of 52 (years) and 104 (years) may have come from the older calendar of the 260c reckoning would seem to be logical from an historical perspective. Nonetheless, those same cyclical periods remained relevant to the 360c.

Such a system of reckoning would then serve in making calculations of whole cycles between one calendar round and another. For, as some authors have pointed out, ancient cultures were very much concerned with identifying the relationships of the cosmos in terms of whole cycles: "The essence of this mathematically predictive astronomy consisted of the art of defining how many whole cycles of one set of phenomena accorded with how many of another set. Maya and late Babylonian astronomers alike were engaged in exploring and discovering commensurate numbers, embedded in nature, that described cycles of recurring phenomena: 99 moons and 5 Venus cycles, 151 Mars cycles and 284 years, the eclipse cycle of 223 moons and 19 seasonal years, and so on." (Aveni, p. 123).

A general belief existed that patterns existed in nature, and that these patterns could be and were expressed mathematically. In this sense, the Table of Numbers of the distinct calendar rounds (360c and 260c) reflect the systematic study of the solar system. The respective counting systems by their very logic of cut-off points are a product of that concern. Let us examine a specific relationship of equivalency between the 260c and 360c:

1872000 ÷ 260 =
7200
rounds
93600 ÷ 260 =
360
"
4680 ÷ 260 =
18
"
260 ÷ 260 =
1
"
13 ÷ 260 =
.05
" (= 1 day)
1872000 ÷ 360 =
5200
rounds
93600 ÷ 360 =
260
"
4680 ÷ 360 =
13
"
260 ÷ 360 =
.72222
"
13 ÷ 360 =
.03611
"
Conversions: 7200/260c = 5200/360c 18/260c = 13/360c

Further considerations of an infinite number of time-cycle relationships could be as follows:

13 rounds of 360c = 18 rounds of 260c
= 8 rounds of Venus (less 8 days)
= 6 rounds of Mars
= 158.5 lunar cycles (less .5 a day)
  etc.

In other words, the relationships that exist in nature, as the planets revolve around the sun, in relation to one another, may be expressed numerically. This possibility seemed to convey a hidden meaning that could be revealed in the pattern of numbers themselves. Students of numerology might make it appear as though only the numbers are significant. But, let us remember that ultimately the relationships that are being measured and converted to numerical expression are what is important. But, the numbers, being the reflection of the relations, take on that same sacredness.

In order to better comprehend the numbers and the relations that they reflect, let us review the distinctions in the counting systems.

As was mentioned earlier, the cut-off point the Table of Numbers is the first place of the third positional level (III, 1). One might initially consider that the very distinction lies in the two system of multiplication; that of 13 x 20 and that of 18 x 20, which forms the distinguishing aspects of the two calendar counts. As we have explained, levels I and II are easily translated between themselves, and then, as a separate set, levels III, IV and V are translatable among themselves. And, note that this occurs equally on the 260c calendar, although the cut-off point is now distinct (260c; not 360c). Furthermore, now all of the levels III, IV and V are divisible by the number 260.

The Table of Numbers, then, as it must have been originally designed, can accommodate any number of an orbital cycle (or day-count), of any particular planet (or moon,s orbit), in order to create a set of numbers relevant to that astronomical body. In a very real sense, then, not just a numbering system or a counting system was created by the 13 x 20 or the 18 x 20 reckonings, but the basis for creating astronomical tables was developed through a method of procedure as we have attempted to show.

Hence, it is at the positional level of III, 1 that the time-cycle number of 360 or 260 may be substituted for that of the orbital time of any other planet. Now, since the Table of Numbers functions on the basis of the integer 20 (as one of its main multipliers), then it is necessary to maintain that the chosen orbital day-count number be an even number (divisible by 20), while the other main multiplier may be any even/odd integer.

Let us now substitute the 260c and the 360c numbers for those relating to other planets in the solar system that were considered to have been known then.

Continued Part III

 

©1995-2003 Copyrighted by Charles William Johnson. All Rights Reserved
Reproduction prohibited without written consent of the author.


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