Earth/matriX Science in Ancient Artwork

The Companion Numbers:
The Ball Game

## Science in Ancient Artwork SeriesNo.45

### New Orleans, Louisiana.

Dedicated to Dylin

The Companion Numbers: The Ball Game
Introduction
• The Companion Numbers of the maya and the Sothic Cycle Numbers
• The 1066000 Number and the Ball Game
1066000: Decimal Sequential Ordering
1066000: The Four-Folud Decimal Sequential Ordering
• Observations

# The Companion Numbers: The Ball Game

Extract
 In this essay, the author explores the possible relationships between the maya companion numbers (1366560; 1385540) and the numbers of the ancient Egyptian Sothic cycle (533265; 1066530). These historically significant numbers appear to be related to numbers which also involve the translation of the distinct day-count calendars (260c, 360c, and 365c) among themselves: 1066000. This particular number appears to be very close (with a difference of only 530 days) to the total sum of days of two Sothic cycles. By interpreting this particular number onto a grid of squares, one observes a design which ressembles that used for the layout of the sacred ball game courts in ancient Mesoamerica. In this sense, the lenght of the ball court would be roughly the equivalent to four Sothic cycles (4 x 533265 = 2133060). The author thus attempts to show a possible relationship between the numbers of the ancient reckoning system and the designs of ancient artwork. A strong case is made to illustrate the possibility that many scholars have maintained for a long time, that the mathematics of ancient science may have been translated into the geometry and the art.

# THE COMPANION NUMBERS: THE BALL GAME

By
Charles William Johnson

Introduction

In this essay we shall attempt to comprehend the function of the companion numbers (1366560 and 1385540) of the maya long count in relation to the number corresponding to the Sothic cycle (533265 and 1066530) of ancient Egypt, in relation to the floorplan design of the sacred ball game of ancient Mesoamerica.

Throughout the Earth/matriX essays, we have been postulating the idea that there exists a strict relationship between the mathematics of the ancient reckoning system of time and the geometrical and artistic expression of ancient works. We have published in this series mainly references and analyses regarding the cultures of ancient Mesoamerica and ancient Egypt, although our researchwork covers a much broader area, whose results we hope to make public in the near future. As may be observed in the series of essays already published, each theme requires a detailed analysis, which at times may appear tedious because of the 'numbers' involved in presenting the material. However, any understanding of the visual aspects of ancient artwork would appear to require such a precise treatment. Much of the artwork may appear to spontaneous at first sight, but as we have attempted to illustrate, the preciseness reflects a knowledgeable precision in concept and conception. It would be possible to examine the many images that appear in ancient artwork, but without the reference to the numbers, very little might be comprehended as to how such images were achieved.

The example that we shall examine and illustrate in this essay might serve as a stepping stone for comprehending the relationship of numbers and the division of space in the design of the sacred ball game of Mesoamerica. It is impossible to state that what is presented herein actually represented the way in which the floorplan design of the ball game was created. That is not our pretention. Simply, we are exploring the function of the companion numbers of the maya and the Sothic cycle numbers, and illustrating a manner in which they may have possibly been linked to some basic designs of the ancient cultures of Mesoamerica.

We may never know where many of the ancient designs came from. However, the manner by which such designs may have been related to the ancient reckoning system may be suggested in this particular method of analysis to some degree.

The Companion Numbers of the maya and the Sothic Cycle Numbers

The companion numbers of the maya long count which are of interest to us for the purposes of this analysis are those of

 1366560 and 1385540

The exact meaning of these numbers has never been agreed upon by scholars in the field. The numbers are obviously related to many of the historically significant numbers of the maya long count and have been discussed extensively in relation to the ancient reckoning system of Mesoamerica.

In a previous essay (Earth/matriX No. 44), we have pointed out how the particular number 1366560 ressembles the number that corresponds to the total number of day in two Sothic cycles of ancient Egypt's time reckoning system 1066530. The difference between these two numbers is intriguing: 300030 days, which represents 822 years of the 365 day-count (very close to the 819c of the ancient maya).

Other authors who have studied the companion numbers of the maya long count, such as Jose Arguelles (The Mayan Factor), have also pointed out the historical significance of another number of the maya long count: 1872000 days. Let us examine the computations around this particular number as of the 360c of the maya long count:

 5200 x 260 = 1352000 days x 360 = 1872000 x 365 = 1898000 x 365.25 = 1899300

The previous totals refer to 5200 years/cycles of each corresponding day-count, expressed in days.

The difference of the number of days from one day-count to another are as follows between each pair of day-counts:

 5200 x 260 = 1352000 +520000 x 360 = 1872000 +546000 x 365 = 1898000 +547300 x 365.25 = 1899300

In order to obtain the differences in the day-counts, one would simply multiply the total number of years involved in the computation, 5200 in this particular case as follows:

 5200 x 100 = 520000 x 105 = 546000 x 105.25 = 547300

in a correspondingly manner for each specific day-count.

The interesting part of the analysis, however, would appear to come from adding up those particular differences, as in the following numbers:

 520000 520000 + 546000 + 547300 1066000 1067300

The number 1066000 is strikingly close to the number that corresponds to the total number of days in two Sothic cycles of ancient Egypt's reckoning system: 1066530. Consider the following differences:

 1066530 (Sothic) 1066530 (Sothic) - 1066000 (maya) - 1067300 (maya) 530 770

Further consider:

 520000 546000 + 547300 1613300 days 1613300 / 18980 = 85

18980 days equals a 52-year period/cycle of the 365c. Now, consider the following:

 1366560 1385540 - 1613300 - 1613300 246740 227760 246740 / 18980 = 13 227760 / 18980 = 12

The difference between 246740 and 227760 is obviously 18980 days, which corresponds to a 52-year cycle (365c).

Now, let us observe the varied relationships of these numbers:

The number of relationships among the maya long count numbers and the numbers of the Sothic cycle, as a function of their particular differences, as may be studied from the previous sets of computations, appears to be andless. All of the numbers appear to reflect the same inner logic. The numbers "chosen" for the Sothic cycle and for the companion numbers of the maya long count of Mesoamerica would indeed appear to reflect the reasoning of a single system of time reckoning. The choices are not only based, then, on a particular 360c day-count, but rather specific chunks of time have been singled out for the computations and are apparently interchangeable among themselves.

The function of the companion numbers, then, serve for making translations from one particular day-count to another.

The 1066000 Number and the Ball Game

We have already illustrated how certain numbers of the ancient reckoning system may be translated into geometrical patterns on a grid (Earth/matriX No. 43). Let us follow the decimal ordering procedure with respect to the 1066000 maya number, resulting from the translation of the 260c calendar to the 365c calendar as previously analyzed herein.

1066000: The Decimal Sequential Ordering

The particular pattern/design that results from placing the coordinates of the number 1066000 on the grid reveals a straightline design that when unfolded in four directions produces a basic design that ressembles that of the floorplan for many of the ball game courts throughout Mesoamerica.

1066000: The Four-Fold Decimal Sequential Ordering

Observations

The computations reviewed in this essay would appear to reflect a direct relationship among the companion number of the maya long count and the numbers of the Sothic cycle of ancient Egypt. Such an apparent relationship would seem to support the idea that these particular time reckoning systems may be much more interrelated than has been previously thought.

Furthermore, the maya number 1066000 distinguishes the amount of days between the 260c and the 365c calendars over a cycle of 5200 years. The gridwork design produced by that number further ressembles the basic design employed in many of the sacred ball courts of ancient Mesoamerica. In this sense, the interpretation could be made that the ball court, along this particular design, reflects a 5200-year period of the three different day-counts, going from the 260c to the 360c (520000 days) and from the 260c to the 365c calendar (546000 days).

One could imagine the ball game reflecting the transition of time from one 5200-year cycle to the next by way of the different day-counts. The interpretative possibilities are andless, as imaginative as the ancient reckoning system itself reveals.