ANCIENT AFRICAN ASTRONOMY (Part 3)

Rada Higgins, Ph. D. mathematics

One of the most famous diagrams, the 3x3 MAGIC SQUARE, and its significance in astronomy

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And important property of the MAGIC SQUARE is that the numbers in every row, column and diagonal sum up to the same integer: 15.

Another aspect of this diagram is that it is a figure-8 representation of the Magic Square Circle. Another figure-8 or S-path representation of the Magic Square Circle is the one below, obtained when we enter the sequence, starting at a place other than a corner (or the center). It is not a Magic Square, but the numbers on every line through the center sum up to 15:

The S-path starts at "6" moves up to "1," around and across the diagonal from "3" to "7" and then across to "4" and up to "9" (and eventually back to "6") as seen below:

This path traces out the same sequence of numbers traced out as we move counterclockwise around the Magic Square Circle (see Part 1), starting from "6."

The Magic Square Circle can also be traced along the sides of the MAGIC SQUARE, giving the following (indented) circular path:

The examples above represent a fundamental relationship between space and time, as will be seen better later.

If the numbers "2" and "8" are interchanged in the 3x3 MAGIC SQUARE, then we obtain a variation of another ancient diagram, Fu Hsi's famous PRE-HEAVEN DIAGRAM of the I CHING, namely an S-path of the integers, in increasing order from "1" to "9:"

In the original PRE-HEAVEN DIAGRAM, the center square is left unnumbered and "5" is moved to the position of "6," "6" to the position of "7" and so forth, giving an S-path of numbers from "1" to "8," with the center (sub) square left unnumbered.

In the I CHING, the numbers on the PRE-HEAVEN DIAGRAM below are represented by trigrams. (According to a few authors, Fu Hsi was Ethiopian or African. Fu Hsi was evidently the name given to the generic group of Ethiopians and Egyptians from the Babylonian region of Africa.)

FU HSI'S PRE-HEAVEN

FU HSI observed that, if an unbroken bar represents "light" or "brightness" and a broken bar represents "shadow" or darkness, then the sequence of trigrams on the PRE-HEAVEN DIAGRAM, as seen from a hypthetical observer outside of and below the circle, visibly resembles (with slight exception of "3" and "6") the phases of an interior planet as it approaches earth, comes into conjunction or opposition with earth and them moves away from earth. The sequence of trigrams also resembles the binary expansions of the numbers from 0 to 7, if broken bars are associated with 1's and unbroken bars are associated with 0.

Along the S-path (see illustration above) through the PRE-HEAVEN DIAGRAM is a well-ordered sequence of increasing integers from 1 to 8. (I the 3x3 square array version of PRE-HEAVEN, the numbers proceed from 1 to 9.)

The integers from 1 to 8 can be viewed naturally as a well-ordered sequence of "spatial" values or "events," namely the sequence of increasing numerical magnitudes.

Moving around the boundary or outside of the circle in a counterclockwise fashion, starting from the top, is a well-ordered sequence of natural "time" events, namely the sequence of phases of a planet (coming into conjunction with the observer) as they proceed from the past (at "1") to the present ("8") to the future ("5").

In part 4, we will see how this relationship between numbers around the boundary of the MAGIC SQUARE and numbers along an S-path through the MAGIC SQUARE might have been used to determine the structure of the solar system and to help in the creation of a Zodiac and the construction of the first 12-month calendar in ancient Egypt. CONTINUE