The Sun, Moon And Stars Of Heaven

The sun, moon and stars of heaven in the text all refer to octal groups. They are related in context to the "sea" extensively mentioned in the book of revelation. We have already defined the "sun" as the original octal, our reference point or origin - our entry point into the symmetry if you will. The "sun" octal used in this section is comprised of K4 subgroups each containing 0 with each of the following triples. {[a,b,c], [a,d,e], [a,f,g], [b,d,f], [b,e,g], [c,d,g], [c,e,f]}.

The "sea" is properly composed of every possible octal. (We may without loss of generality in the text simply restrict ourselves to the same seven symbols "a" to "g".) There are then a total of 30 octal groups.

The "stars" are perhaps the next easiest to define. They are composed of the elements and K4 subgroups likewise of every possible configuration of seven symbols (with zero) into GF(8). Thus whether octals are composed of K4 groups or singletons from the 30 octals, then these additive elements are properly the "stars". This is a definition exclusive of the "sun" as an "origin". (as it represents the full octal.) We may note also that under our K4 addition of (A v B)^c the octal may act as if it were zero.

So we may divide the sea into the "sun" part and the purely "stars" part wheras the "sea" is the set of both and all. The sun octal is taken as only to be the right handed octal, the left hand is comprised from the stars.

The moon is somewhat harder to define but it is worth noting that the moon may shine in the day or in the night. The left hand corresponding to the sun octal (as the right) under one seven cycle may be the right hand of a further right/left pair under a different seven cycle. The first generation would be the "sun", the second the result of the left hand which is the second generation (The moon) which has a further generation or left/right pair comprised of a third octal in the sea, and this third generation would be "of stars".

Then there are three octals, (sun/moon) and (moon/stars) and (stars/(more stars)) in their right/left pairs. We can note that there is no octal paired with itself as right/right. that is, the complement or coset of a K4 subgroup must contain its corresponding triple in the left hand, there is no "moon/moon" middle generation. However we also note that it is only considered that the right hand is "shining" as an octal. At this stage the left hand is merely made of sets of triples, not under addition. Properly then these three generations are made of "sun", "moon", "stars".

Finally we note that the sun may shine without the moon and the stars likewise. But the "moon" may not shine on its own: it would be required to be present as both "left and right" under its definition as an interface as between left and right. If we consider each generation on its own, we have redefined the "moon" as either a "sun octal" or "a set of stars".

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