As By The Holy Spirit
In the sets of octals, the Holy Spirit is obviously as multiplication; yet in the sets in a disjunction the Holy Spirit is not clearly apparent.
Instead, any arrangement of the seven K4 groups within the octal may form those disjunctions (in the principal elements) of the sets of positive predicates without loss of that embedding. The "weakness" of the Holy Spirit is the unity element, or that of "rest" itself - the sabbath, if you like.
Unity corresponds to virtue; that weakness of C7 being equivalent to the axiom of virtue holding firm, for without it there is found no octal at all, and no disjunction then holds in positive properties as there is a failure of mutual privation between them.
Again, God's strength is made perfect in weakness. Any operation of multiplication valid over an octal may cycle the elements, and every element in every field GF(8) can become as virtue; though it is somewhat the case that the Holy Spirit may alter the schema of the sets in the disjunction - as long as the subgroups in the octal are also preserved.
For instance, r ∨ p&r^{-1}=>s requires all three sets to be necessarily positive; it is then the case that N(Pos(p&r&s)). From this I may attain N(p&r&s) for a Godlike being and then also N¬(p&¬(r&s)) for that disjunction, or indeed any other in the three! Yet how would I map between them? For a disjunction exiting the right side I require "p & ¬r & s", it is positive and necessary for the axiom of virtue to hold, so I can force any predicate λ on p, forming N¬(λ&¬p). That stated, I can permute the initial schema "p & ¬r & s" any way I wish!
So, if λ=>p I may always consistently put λ=p&r&s, with N(Pos(λ)). Given then, N(Pos(p&¬r&s)) with N(Pos(p&¬r)) by axiom of virtue (binding of virtue) and with the distributive law for the perfect I then find N¬(¬p&r&¬s) the result. Then N¬(r&¬p&¬s) holds with r as virtue bound within the disjunction of p ∨ s.
So, there are potentially three cycles in the disjunctions of virtue. This would hold in the K4 form alone; there is no subfield GF(4) in GF(8), though the Frobenius map does hold a three-cycle over the static subgroup.
Now, the really good bit!
As seven cycles preserve the subgroups in the octal, these disjunctions in these sets r, s, u, v, etc., are all preserved in another disjunction under that product of C7, but due to the schema they each appear shifted as if by a three cycle as above!
So under the cycle (a, b, d, c, f, g e), if p=a, r=b and s=c, then these quite possibly become as b, d and f; and the subgroup is quite possibly mapped to the sets in disjunction of {(r&s)^{-1}, r, u^{-1}}. However, this leaves them able to be "skewed" by just such a three cycle as above, so that "r" then acts as virtue (the product of the seven cycle on "p" before) instead of (r&s)^{-1}.
As the seven cycle may be one of eight, as there are a possible 84 schemas (42 of which oppose as wormwood), that leaves 42 possible schemata; and as also in the mystery of the seven golden candlesticks; every schema is mapped by a seven cycle through the other seven groups of seven cycles, sharing one unity (identity element) between them.
Then in order for the Holy Spirit to so act, there is one condition, that of binding in the axiom of virtue; that N(Pos(p&¬r&s)) with N(Pos(p&¬r)) on one side of the disjunction r ∨ p&r^{-1}=>s.
Then the completeness of the Holy Spirit is found (perfected) in the axiom of virtue; that being the existence of the "sabbath" or unity in C7.
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