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The Third Part Of...

The text repeatedly uses the phrase "the third part of...". It has become apparent that this does not refer to a third as a fraction, but the consequence to two elements in product. The definition for a binary operation on a set S is that for all a, b "elements" in S there is a one to one map; mapping all ordered cartesian pairs of the form (a,b) onto an element of S. Some texts use the notation S x S => S, meaning "from the cartesian product S x S into S."

An example could be for any two whole numbers, adding them together gives another whole number. Also, two fractions (with whole numbers in a and b of the form a/b) in product, produce another fraction.

We see then that the "third part" that is "hurt" or "destroyed" is such that the product of elements in the groups in view is disrupted, not present or is impossible.

Then from the trumpet sequence we see that the third part of trees burnt up would disrupt the product of subgroups so that (A v B)^c is no longer a valid subgroup.

All green grass burnt up reveals that "small trees" i.e. singletons also have their operation removed (The left handed octal has no intersection of a whole K4 subgroup with the right hand) The octal operation is completely disrupted.

The "third part of the sea" refers to a binary operation between differing octal groups: However it is not "destroyed" but becomes defined based on intersections (as blood). The third part of creatures in the sea (singletons) were destroyed - there is no operation on them in agreement with the "sun octal". The third part of the ships refers to "trees" as it were, but in the sea. There is no agreement in the operations on subgroups either!

Now with the fourth trumpet there is more to find on "the third part". We see the subject changes to "waters" rather than the sea. Within each octal in the sea (i.e. with the "waters") there is hidden a correspondence not between pairs of the "syzygy" (singleton/fire/hail) from each element but between triples of these syzygy elements, with the third part become the internal correspondence that allows a "fourth" octal to become as it were "the ring of truth" or a "filling in".

That "filling in" seems in accord with the other three octals which share two syzygy elements with each other. The alignment of this fourth octal based upon the generators (fountains in the sea or rivers on the land) of the other three octals found from the "third part" within each octal set allow a "stronghold" as it were, a "great delusion" a seeming place of rest and safety.

We actually have found the operation where the dialectic comes into play! However we relate with "wormwood" the internal operation of the earthly elements {d,e,f,g} (if [a,b,c] is static) in the manner that each set of three elements is aligned similarly with the fourth. One is "unity" or fixed and the other three represent the three elements of the balances that correspond in triples to the singletons that are not unity. The difference here is that the dialectic is formed of triples of octal generators instead of those elements that are singletons. It is however the very same device.(we note that any three of the elements {d,e,f,g} as above are such generators of an octal.} The presence of a fourth "hidden within" is the same device as the "Wormwood" of the text.

The possible combinations of these wormwood sets number 666 also in the sea, as does the pale horse of the seals. Hell "follows after" in this system - we see them revealed in the fifth and sixth trumpets. We conclude that Death is actually named "Wormwood". Many men were killed by this bitter water - a good analogy for antichrist as opposed to the living water given by Christ.

The third part of the Sun, Moon and Stars are easily related. Upon writing a sun octal and then the left hand; rewriting the left hand as it were a new right hand (with a different unity) and repeating for a third generation we see we now have three separate "sun octals" as it were based on three generations, the first the "sun" the second that is present in both as left and right hand, and the third as the "stars". The second is present with both sun and stars which we call "the moon". Then we note that we have a third missing in each column of this table...

.............Sun.......Moon......Stars
Sun..........E............E..............
Moon......E...........................E
Stars......................E.............E

The stars are not present in the "day" and the Sun is not present in the "night". What is harder to see is whether the moon could "shine" on its own. Not, if it had to be a moon where the left and right handed parts were the exact same octal! This may seem trivially obvious, but remember that the additive structure between right and left hands is in octal reversal. It is impossible therefore to have the structure reversed with the same elements, under a single seven cycle. (Otherwise we would require a pair of K4 subgroups to have no intersection!).

So therefore a "third part of the moon" is also smitten.

This trumpets verse is easily explained away by noting that for the stars to not equal the day (reversing left and right) , we require a different choice of unity. It is then impossible to form a right/left pair from the sun and star octals. The result is that there is no operation given in the text that forms a "righteous" system of the "sea" other than in the isomorphisms of the 24 elders in GF(8) to the "sun octal". There are many octals in the sea and only one is in good favour with God: picking and choosing one's spiritual dwelling without settling is not the same as salvation.


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