Earth/matriX
Science in Ancient Artwork
by ©Charles William Johnson
The 360c Square: A Design
One of the most striking aspects of ancient artwork is the geometrical nature of many of the designs and patterns. Geometry is translation of numbers into spatial configurations. Hence, the study of the logic of numbers of the ancient reckoning system serves as a sound basis for considering the nature of certain designs and patterns. For, as we shall observe in this essay, it is possible to consider the artwork as of specific numerical progressions and mathematical models. Many authors have examined ancient artwork precisely from the perspective of its possible mathematical expression and translation. We shall consider similar ideas in this essay.
Once we observed the pattern that obtained from the 36c square listed above, we considered the possibility of creating squares that would reflect other numerical combinations. But, before we effected the analysis of other numbers, we constructed a possible pattern as of the 36c square itself.
It is well-known that the ancients considered the number 4 to be extremely significant; especially, the idea of the four directions (not to mention up and down for now). Therefore, we proceded to take the 36c square pattern that was derived from the 36c square itself and repeat it four times for every direction on the grid. The following pattern was observed:
Basically, the essential pattern revealed by the 36c square is revolved on its innate axis for each side of the grid. The pattern that evolves is quite suggestive of many designs found in the historical record, especially of the ancient cultures of the Western hemisphere, although one may perceive similarities of design with the artwork from other cultures around the world. It all depends upon how one views the pattern produced on the grid; that is, which elements are viewed at a particular moment and from a specific perspective. The most obvious aspects of the pattern are the four pyramid-like structures or profiles that are produced, and the central crisscross axis.
Other aspects that come to mind immediately are the quatrefoil-like patterns and the parquetry-like designs of ancient times. But, even more recognizable are some of the specific designs employed on the pyramids of the different cultures of ancient Mesoamerica; the grecas, the repeat patterns that line the walls of those pyramidal structures.
A possibility that has always impressed us is to consider the grecas as having a particular numerical value or valence, representing specific relationships among the planetary bodies. In the following illustrations, we shall be able to perceive and recognize other configurations that are highly suggestive of some of those ancient designs on the pyramids of Mesoamerica.
The 36c square pattern, in its single presentation, is obtained by filling in the corresponding square on the grid in the following manner.
Column one: all squares are filled in; each value occurring once.
Column two: squares 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36 are filled in on the grid.
Column three: squares 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 are filled in.
Column four: squares 4, 8, 12, 16, 20, 24, 28, 32, 36 are filled in
Column five: squares 5, 10, 15, 20, 25, 30, 35 are filled in.
Column six: squares 6, 12, 18, 24, 30, 36 are filled in.
Column seven: squares 7, 14, 21, 28, 35 are filled in.
Column eight: squares 8, 16, 24, 32 are filled in.
Column nine: 9, 18, 36 are filled in.
Column ten: 10, 20, 30 are filled in.
Column eleven: 11, 22, 33 are filled in.
Column twelve: 12, 24 are filled in.
Column thirteen: 13, 26 are filled in.
Column fourteen: 14, 28 ....
Column fifteen: 15, 30
Column sixteen: 16, 32
Column seventeen: 17, 34
Column eighteen: 18, 36
Column nineteen: 19, 38
Column twenty: 20
Column twenty-one: 21
Column twenty-two: 22
Column twenty-three: 23
Column twenty-four: 24
Column twenty-five: 25
Column twenty-six: 26
Column twenty-seven: 27
Column twenty-eight: 28
Column twenty-nine: 29
Column thirty: 30
Column thirty-one: 31
Column thirty-two: 32
Column thirty-three: 33
Column thirty-four: 34
Column thirty-five: 35
Column thirty-six: 36
More simply stated: each column is an expression of its own number, added to itself in progression. However, we wished to offer the corresponding numbers in order to be able to visualize the patterns numerically. In this essay, however, we shall attempt to visualize the patterns in terms of space; not numbers as such.