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is consigned to the bottom in the picture.
And this portion
is consigned to the top.
(Also, in the PRINCIPLE OF OPPOSITES DIAGRAM, "5" is replaced by "7"--producing a total of two "7"'s, which looks like a mistake. But is it? This so-called "mistake" makes the viewer consider all the other possible arrangements the PRINCIPLE OF OPPOSITES DIAGRAM might have had, thus it makes the viewer search for clues as to how to interpret the diagram, letting us know that the diagram is a cryptic code.)
Returning to our previous discussion, one consequence of this choice of arrangement (above) is that the progression of integers from 1 to 8 is switch from clockwise (in the PRINCIPLE OF OPPOSITES DIAGRAM) to counterclockwise in direction.
Another consequence of this arrangement is that a square inscribed inside another square is produced. The ancient Africans used the method of inscribed squares to generate or produce magic squares. Many examples of these constructions were given in an Arabic manuscript attributed to a native of northern Nigeria, Muhammad ibn Muhamad (see AFRICA COUNTS, Claudia Zaslavsky, Lawrence Hill & Company, 1973). Subsequently and subconsciously, a viewer is prompted, while looking at the PRINCIPLE OF OPPOSITES DIAGRAM to see a CLUE giving a square of 4 numbers, situated diagonally, within a larger square of 4 numbers. Considering all the triangular shapes, constituting the pictogram of the PRINCIPLE OF OPPOSITES DIAGRAM, which could be arranged in groups of 4 to form an inner (diagonal) square, (in unraveling the code of the PRINCIPLE OF OPPOSITES DIAGRAM), one promising candidate is the one depicted below, with the numbers 1,2,3 and 4.
The remaining pieces left over can then be arranged to form an outer square of larger numbers: 5,4,7 and 8.
In the PRINCIPLE OF OPPOSITES DIAGRAM, instead of 5, 6, 7 and 8, there are two 7's in the bottom row. On one hand, we are prompted by this to either replace one 7 by a 5, giving the case we have just been considering or, alternatively, we might be prompted to replace one 7 by a 9, suggesting another situation. In this case, the outer square of larger numbers would be the one depicted below:
In this case, the missing or invisible "5" value can be thought of as being at the center of the pictogram. Setting the smaller square inside the outer one, in this case, gives the mirror-image of the Yellow River arrangement of numbers (seen below), but since the numbers of the original PRINCIPLE OF OPPOSITES DIAGRAM progress in a counterclockwise fashion, this induces us to flip this diagram in the vertical plane, producing the conventional Yellow River Diagram.
(To sum up, the significance of the two 7's is that one of them must be replaced by 9, to give the key to the correspondence between the PRINCIPLE OF OPPOSITES DIAGRAM and the YELLOW RIVER DIAGRAM. If, instead, the other 7 is replaced by 5, then, in essence, the PRE-HEAVEN DIAGRAM (coming up) is obtained. In this article, it won't be undertaken to develop a rigorous proof of these conjectures, but it reasonable to propose that a "topological-type" correspondence exists between the PRINCIPLE OF OPPOSITES DIAGRAM and the YELLOW RIVER DIAGRAM by a mathematical argument of the following type: Let each numbered region on the PRINCIPLE OF OPPOSITES DIAGRAM correspond to a numbered point on the YELLOW RIVER DIAGRAM. In moving (in clockwise fashion) between successive and/or increasing integers, the transversal of a diagonal lineof positive slope in the upper region of the PRINCIPLE OF OPPOSITES DIAGRAM corresponds to a transversal (in counterclockwise fashion) of a horizontal (X-) axis (positive) through the center "5" on the YELLOW RIVER DIAGRAM. Similarly, the transversal of a diagonal line of negative slope corresponds to the transversal of a vertical axis (negative) through center "5" on YELLOW RIVER. Transversal of a horizontal line, from a lower region to an upper region, such as in the case of proceding from "8" to "1" requires the transversal of the line y=x (on negative values). Transversal of a vertical line requires the transversal of the line y=-x, etc. And vice-versa. Applying this reasoning, it becomes clear that the two pictograms belong to a single category (a proof of this will not be undertaken here.) It was observed earlier that the inner "square" of the PRINCIPLE OF OPPOSITES DIAGRAM is placed diagonally within the outer square. Applying this to the two arrays of numbers from the PRINCIPLE OF OPPOSITES DIAGRAM, we obtained above (and also to the numbers of the YELLOW RIVER DIAGRAM), we generate the Magic Square Circle array of numbers (seen before), which we will discuss more about in part 3. CONTINUE