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Possibly 9 intervals of time were important, because of the models of PRE-HEAVEN, the PRINCIPLE OF OPPOSITES DIAGRAM and the YELLOW RIVER DIAGRAM, which all utilize natural numbers from 1 to 8 or 9, which can be conveniently arranged in a 3x3 square array. The number 8 was a natural value that arose from a natural "binary" phenomenon of nature, namely the 8 obvious phases of a planet representable by trigrams, a primitive (and binary) way of writing the numbers from 0 to 7.
In thinking about planets lined up on a fixed ray from the sun, it soon becomes apparent that a fixed ray would move differently (Kepler?) for each individual planet viewing it. Jupiter, however, might be the best candidate for a planet representing the "mean" (or average) planet among all the planets. We also notice that it takes 12 years for Jupiter to make one orbit around the sun. Every year, when earth returns to the same place on its orbit, Jupiter has moved 1/12 around its orbit.
During a cycle of kI days, where k=1,2,...10, the successive positions taken by Jupiter as seen by a stationary observer outside of its orbit, starting from the point furthest from pending opposition, will be subscripted with the numbers of the Magic Square Circle: J6, J1, J8, J3, J5 (J5 would be positioned next to the starting point, J0), J7, J2, J9, J4, (J10 would be positioned next to J5). J12, if we were to continue, would be almost exactly at the starting point, J0.
For simplicity, J10, J5 and J0 are identified with the fixed observer's position and and with earth in opposition with Jupiter and are brought inside, to the center of the circle or orbit. (Thus the orbit along which Jupiter travels, as viewed by an observer on earth, is seemingly an indented circle or heart-shaped curve.)
Using our own imagination, it seems plausible that a real observer viewing Jupiter's orbit (or the Zodiac) from the earth should only see 1/2 of Jupiter's orbit for half a year. Earth must be on the other half of its orbit, and hence oriented in the opposite direction to observe the other half of Jupiter's orbit. During the night, from a fixed ray, as well, it seems logical that only half of the celestial vault would be actually be visible. The other half of the celestial vault would be viewable only when earth was on the extension of the fixed ray, through the sun.
In general a set of events which occur in an (indented) circular arrangement on a planar calendar, occur as an S-path (or figure-8) arrangement in the 3-dimensional time-space continuum.
Putting the 2 pictures together produces a composite ultimately equivalent to putting the Magic Square Circle in an "S-path" or figure-8 configuration in a 3x3 square array, thus as a MAGIC SQUARE:
Interchanging P2 and P8 and observing (hypothetically) from position P9, we would be viewing the planets along an alternative S-path (say, S'-path) through the sun, in the exact order their time events occurred on earth, (but not from the original perspective of earth on a fixed ray, in opposition with Jupiter). The S'-path would thus be a variation of the PRE-HEAVEN DIAGRAM, mentioned earlier, which uses 9 values instead of 8. Therefore, with respect to this PRE-HEAVEN DIAGRAM, the observer or earth is really an internal, existent viewer at the center of the diagram rather than an ideal, external or hypothetical viewer outside of the diagram.
To summarize, interchanging P2 and P8 gives the sequence of events as they occur in time (to an observer, at the center, on Jupiter or earth), as opposed to how they occur in time, relative to an observer, hypothetically outside and external to Jupiter's orbit.
For the sake of completeness, it might be noted that the paths S and S' above form a "swastika" with respect to each other (the angle between their axes being 45 degrees).
As conjectured earlier, if the 9 values on the S'-path of the PRE-HEAVEN DIAGRAM represent a well-ordered sequence of "time" events, then, inversely, the sequence of values around the boundary of the diagram apparently represent a well-ordered sequence of "spatial" events and vice-versa. (In the original observation, the "time" events (phases) were situated on the boundary of PRE-HEAVEN and the "spatial" events (magnitudes) were on the S-path through PRE-HEAVEN.)
How can this conjecture be verified? I propose that it was verified and demonstrated in antiquity by utilizing the Metonic cycle. A study of this theory could have been scheduled to coincide at a time when the planets were all in conjuntion on a fixed ray. Also, a study of the relationship might reasonably have been initiated during a time of solar eclipse, with Jupiter in conjunction with the earth (estimated at night, by the light and position of the full moon )or during a time of lunar eclipse.
Thereafter, as seen before, at intervals of I, Jupiter would land on one of 12 positions on its (relatively heart-shaped) orbit, selecting these positions out, in such a way, that the first 9 or 10 positions would form a well-ordered sequence (according to time of occurence) of positions subscripted with the values of the Magic Square Circle on a planar calendar. In three dimensional space, the sequence of positions would lie on an S-path through earth, in "opposition with Jupiter," in the center, whose subscripts, if put into a 3x3 square array would form a MAGIC SQUARE ("flipped" and rotated by 45 degrees with respect to the original array of subscripts on the calendar.
Clearly, after the initial time of a simultaneous opposition of all the planets on a fixed ray from the sun, through the earth (and every other planet in opposition with the earth on the ray), if another simultaneous opposition were ever to occur again it would occur at a ray through one of positions taken by Jupiter every I days.
The idea of a "fixed" ray, according to the laws of Kepler, is a relative concept. Since Jupiter is the most likely candidate for the "average" planet, it is reasonable to describe the behavior of the other planets in terms of the "fixed" ray through Jupiter (the ray that moves "on the average" as Jupiter moves every 6939.1161 days, and on which the earth lands again, every 6939,1161 days. (So from earth, we observe how the fixed ray moves on Jupiter's orbit). Technically, this also requires that we define the landing of the planet Pk on the "fixed ray," in terms of its proximity to Jupiter at the interval of kI days. This probably was done "by eye" in ancient times, by noticing when other planets came in opposition with Jupiter. Today, we should be able to determine this by division, using the known periods of the planets. However, the fact that not every planet revolves the same direction around the sun might have bearing on what can be determined. Also, a rigorous definition of "best" division would have to be required, which will not be undertaken here. Whenever a planet returns to the same position where it was, at the time of simultaneous opposition, it lands again on the fixed ray. Because the S-path above, through Jupiter at its center, is symetrical indicates that any "fixed ray" may possibly be of this form. This would naturally have bearing on the definition of "best" proximity. Also, the fact that not all the planets' orbits may not completely be planar should also have bearing on the determination. However, in an initial attempt I made at judging best "division" or "proximity" (to Jupiter) in determining the order of return of the planets to the "fixed ray," (see my copyrighted manuscript "Juggling With Planets" or "A Mathematician's Return to Atlantis," The Library of Congress), I determined that, the sequence planets obtained around the boundary of the S-path through Jupiter, gives, with a little ambiguity, the planets in order of their distances from the sun.
In my opinion, the zodiac, originally, might have been defined in terms of the planets of the solar system, which were used to determine the main constellations along Jupiter's orbit in space. RETURN TO PART 1 This scientific paper is now available on the forum SEND A MESSAGE