The Ships Of Chittim

The passage opens with the verses that depart from the historical account - we enter into the time of the end.

-- Click To Expand/Collapse Bible Verses -- Dan ch11:v29-32
Dan 11:29 At the time appointed he shall return, and come toward the south; but it shall not be as the former, or as the latter.
Dan 11:30 For the ships of Chittim shall come against him: therefore he shall be grieved, and return, and have indignation against the holy covenant: so shall he do; he shall even return, and have intelligence with them that forsake the holy covenant.
Dan 11:31 And arms shall stand on his part, and they shall pollute the sanctuary of strength, and shall take away the daily sacrifice, and they shall place the abomination that maketh desolate.
Dan 11:32 And such as do wickedly against the covenant shall he corrupt by flatteries: but the people that do know their God shall be strong, and do exploits. (KJV)

Now, the north returns and comes toward the south. We do not remove the restrainer yet - rather we show why it is removed. We have the north and south octals in reversal and alignment with the seven cycle acting upon them as;

a = [b,d,f] = {c,e,g}
b = [c,d,g] = {a,e,f}
d = [c,e,f] = {a,b,g}
c = [a,f,g] = {b,d,e}
f = [b,e,g] = {a,c,d}
g = [a,d,e] = {b,c,f}
e = [a,b,c] = {d,f,g}

Now we previously stated that static triples were as "bows" in shape, a three cycle which we draw a little differently - we have a very simple "boat" shape like a child's picture of a hull.

Then the "ships of chittim" we analogously relate to these triples written from-west to east - which we right from east to west (right towards left) in the left margin, (Daniel also write right to left - opposite to myself).

[b,d,f] = {c,e,g} or {a,e,g} or {a,c,g} or {a,c,e}
[c,d,g] = {a,e,f} or {b,e,f} or {a,b,f} or {a,b,e}
[c,e,f] = {a,b,g} or {b,d,g} or {a,d,g} or {a,b,d}
[a,f,g] = {b,d,e} or {c,d,e} or {b,c,e} or {b,c,e}
[b,e,g] = {a,c,d} or {c,d,f} or {a,d,f} or {a,c,f,}
[a,d,e] = {b,c,f} or {c,f,g} or {b,f,g} or {b,c,g}
[a,b,c] = {d,f,g} or {e,f,g} or {d,e,g} or {d,e,f}

Where the triples in {x,y,z} are the "ships" (Which Daniel would write reversed in the right margin as if coming to the northern octal from the west.)

Each column equates to a different choice of unity - and whilst they operate downward, each choice of three columns can not share the same seven cycle as the remaining fourth has with its partner the north (leftmost column).

Thus the ships that come against the north as he moves toward the south (second column from left) interrupt the choice of unity as well as the seven cycle. The king is "grieved" in moving out of his fortress into the centre element "a" in between [b,d,f] = a = {c,e,g}.

So in the southern octal where the static subgroup is [c,e,g] - when the ships come against the north the king is forced to counter them (as different variants of what is "south") and so removes or returns himself to the northern octal in which he has strength against them.

The north then has indignation against the holy covenant - he also has intelligence with them that forsake it - The associations of static subgroups in the north do not oppose the ships as if they were it's cosets - they are not subgroups of any octal (they have two singletons in their intersection) So the Holy Covenant is insufficient to oppose the ships from the refuge of his "fortress" - (the static group in the leftmost column.)

He begins to operate in the spirit of antichrist in the balances formed by shifting unity in the northern octal - in them he finds the triples that are the ships of the top row above. He begins to prepare devices against these sets of triples (ships) that correspond to every "fortress" or subgroup in his own land - the northern octal.

Now we are told "arms stand on his part." We may equate the "arms" that stand to the unity element of the north in the centre - so that each singleton is represented by the three subgroups that contain it.

a = [a,b,c],[a,d,e],[a,f,g]
b = [b,e,g],[b,d,f],[a,b,c]
d = [b,d,f],[c,d,g],[a,d,e]
c = [a,b,c],[c,d,g],[c,e,f]
f = [a,f,g],[b,d,f],[c,e,f]
g = [a,f,g],[b,e,g],[c,d,g]
e = [a,d,e],[b,e,g],[c,e,f]

Then we may "reshuffle" our sets of ships coming against the north by rearranging them so that rather than holding a subgroup static in each row we hold unity fixed and set out four sets of subgroups with their cosets corresponding as;

a = [b,d,f] or [b,e,g] or [c,d,g] or [c,e,f]
b = [c,d,g] or [a,d,e] or [c,e,f] or [a,f,g]
d = [c,e,f] or [a,b,c] or [a,f,g] or [b,e,g]
c = [a,f,g] or [b,d,f] or [b,e,g] or [a,d,e]
f = [b,e,g] or [c,d,g] or [a,d,e] or [a,b,c]
g = [a,d,e] or [c,e,f] or [a,b,c] or [b,d,f]
e = [a,b,c] or [a,f,g] or [b,d,f] or [c,d,g]

Which respectively correspond to the triples
a = {c,e,g} or {c,d,f} or {b,e,f} or {b,d,g}
b = {a,e,f} or {c,f,g} or {a,d,g} or {c,d,e}
d = {a,b,g} or {e,f,g} or {b,c,e} or {a,c,f}
c = {b,d,e} or {a,e,g} or {a,d,f} or {b,f,g}
f = {a,c,d} or {a,b,e} or {b,c,g} or {d,e,g}
g = {b,c,f} or {a,b,d} or {d,e,f} or {a,c,e}
e = {d,f,g} or {b,c,d} or {a,c,g} or {a,b,e}

In defining subgroup addition as (A v B)c we find that each row of these shuffled and reordered ships of chittim in pairs equate to a subgroup of the northern octal in the same row.

i.e. addition on {c,e,g} or {c,d,f} or {b,e,f} or {b,d,g} result in groups in [a,b,c],[a,d,e],[a,f,g] as desired. Thus these "arms" (the groups with "a" within) are successful on the part of the king of the north - they "stand" against the ships of chittim as subgroups corresponding to cosets.

However - that said there is no seven cycle common to the octals of the rows and the octal of the north - there is an incongruity. This is easiest seen in converse - that (a,b,d,c,f,g,e) does not preserve the subgroups of [a,b,c],[a,d,e],[a,f,g],[c,e,g],[c,d,f],[b,e,f],[b,d,g].

Neither is this true for any of these octals - they are acted upon by swapping elements in the northern octal In the octal example just given switching (b,c) or (d,e) or (f,g) suffices.

This swapping or transposition of elements is a "pollution" of the operation of the northern octal (The sanctuary of strength - the operation of singletons in the octal rather that that of n (A v B)c on triples which holds generally.) The operation of the seven cycle is interrupted - (the daily sacrifice is taken away) so that no element can be mapped onto unity using any seven cycle upon the northern octal.

In place of the northern octal is then "the abomination that makes desolate." In opposing the ships of chittim - the intersection of groups [a,b,c],[a,d,e],[a,f,g] between the two octals (using the top row for brevity) may never share a seven cycle with the northern octal, as it would generate the northern completely. There is no intersection so that a = 1 any longer.

How does this remove unity?

Well, if the device is employed universally over every octal then since there is no octal containing only one subgroup of another - (minimally they must share three subgroups) There is either the case where each octal corresponds to left or right (north and south) with no intersection of groups, or either they share three subgroups. (seven is the trivial comparison)

There is then a device that may be universally employed against the operation of the field GF(8) upon it's subgroups. No octal group shares it's operation with another even if they share three subgroups - the definition of the group is different - expecting the intersection to be in the same field negates the idea that there is multiplication defined upon it. That there is no multiplication common to both octals (sharing a set of three subgroups) places the K4 form of the filter in both - (and we know that although in each case the K4 form is valid) yet the octals with their multiplications are inducing the same K4 form, yet these are different "fields" and though isomorphic, they are separate.

The abomination that makes desolate is completed in the dialectic process by the beast and it's image. We expect that the king sets up these octals as thesis and antithesis and works to facilitate in the centre.

Those that do wickedly against the covenant are in view as those with whom the king has "intelligence". Instead of keeping them in place as within the cosets of [b,d,f] (the northern fortress) by shifting unity, they are now present as subgroups in the rows of the reordered ships. The king succeeds in corrupting them - removing them from the proper operation of the seven cycle (in the northern octal) and it's induced three cycle holding them static; to another seven cycle that sets them up as subgroups. He has corrupted their position by "flattery" in raising their status to subgroups.

Those that know their God - those remaining in the northern octal under the original seven cycle remain strong - under the seven cycle the groups that stand against the ships of chittim remain preserved and are a remaining "sanctuary of strength". (Under the original seven cycle (a,b,d,c,f,g,e) we shift through)

a = [a,b,c],[a,d,e],[a,f,g]
b = [b,e,g],[b,d,f],[a,b,c]
d = [b,d,f],[c,d,g],[a,d,e]
c = [a,b,c],[c,d,g],[c,e,f]
f = [a,f,g],[b,d,f],[c,e,f]
g = [a,f,g],[b,e,g],[c,d,g]
e = [a,d,e],[b,e,g],[c,e,f]

And it is these whom do "exploits" - they are the ones with the show of strength against the ships of Chittim, The "king in the centre" analogous to the unity element or the intersection of the three shows very little strength - yet the seven cycle in correspondence to the singleton of intersection cycles the three subgroups in those rows as closed upon themselves. (They are the K4 form of the filter in view. They know God is Jesus Christ.)

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