Casting Up A Mount

The king of the north retaliates in the text and we see a far broader exchange of powers.

-- Click To Expand/Collapse Bible Verses -- Dan ch11:v13-16
Dan 11:13 For the king of the north shall return, and shall set forth a multitude greater than the former, and shall certainly come after certain years with a great army and with much riches.
Dan 11:14 And in those times there shall many stand up against the king of the south: also the robbers of thy people shall exalt themselves to establish the vision; but they shall fall.
Dan 11:15 So the king of the north shall come, and cast up a mount, and take the most fenced cities: and the arms of the south shall not withstand, neither his chosen people, neither shall there be any strength to withstand.
Dan 11:16 But he that cometh against him shall do according to his own will, and none shall stand before him: and he shall stand in the glorious land, which by his hand shall be consumed. (KJV)

We now extend the field from GF(8) to an extension of both GF(4) and GF(8). Finite fields of this order are of degree 6n (for n a positive integer.) In opposition to the forces of the king of the south in his own fortress. 6n is a correct degree of extension, equivalent to "certain years".

Moving on to orbits of the subfield GF(4) in our extension F, we array ranks of the forces of the north by multiplicative cosets of the GF(4) subfield - arrayed in ranks of K4 additive subgroups under the operation of some generator of the field F.

b0 => hb0 => h2b0 =>...hnb0 =>...h-1b0
d0 => hd0 => h2d0 =>...hnd0 =>...h-1d0
f0 => hf0 => h2f0 =>... hnf0 =>...h-1f0

a0 => ha0 => h2a0 =>...hna0 =>...h-1a0

c0 => hc0 => h2c0 =>...hnc0 =>...h-1c0
e0 => he0 => h2e0 =>...hne0 =>...h-1e0
g0 => hg0 => h2g0 =>...hng0 =>...h-1g0

The north comes with "much riches" - i.e. a great deal of equipment, besides a great army - made of the orbits of the static bow in the triple we would think of as {b,d,f}. Many stand up against the king of the south (the elements hna0 in the centre.) Now, if a0 = 1 then unity is not preserved amongst the ranks, but is equal to a power of the generator g. Those that would exalt themselves to the position of a floating unity (the robbers of Daniel's people c.f. the elect.) exalt themselves in this manner as to make the vision true - that there is one whole rank in the centre all unity - and in effect the vision is for a morphism of the field F down to GF(8). However, this is an effort that is sadly frustrated! (Those robbers shall fall.)

There is no homomorphism, For GF(4) a subfield of F, there is a short orbit of K4 in the field of length m = |F*| / 3. Now, when the group is cycled back upon itself it is not done so in alignment - for we actually have a shift of row as we orbit GF(4)+ amongst the field F, so that the effect is that the row shifts one down or up as we multiply by gm. The effect is universal amongst every rank, so the elements in the cosets of GF(4) ([b,d,f]) are aligned in diagonals like "a ramp".

We have the meaning in abstract of the siege ramp (The mount cast up) set up by the king of the north.

Now, every element of the field F is present in such an orbit of GF(4)+. Then the elements of GF(4) enter in part into the fortress of the south, and likewise the "chosen people" (crack troops behind enemy lines) of the south enter the ranks of the north. The result is in both hands symmetric: yet North is attacking south so his best fortress is penetrated. (North/ south were to start pretty much arbitrary, like white or black in chess.)

Now every element in {c,e,g}i is as a "most fenced city". Yet if there are cities within multiple extensions of the southern fortress, i.e. also subfields, there is no subfield in F which the "ramp" or its effect will not have the elements similarly cycle through: (There is no homomorphism (proper and non-trivial) anywhere. There can be no "vision" of separating the elements without the ramp effect. In order to do so we may only multiply by the unique element of unity, and not by a power of a generator.

Therefore no "city" as GF(4) or any subfield in F is safe against the siege "ramp" or "mount".

"He that comes against him" i.e. the king of the north , does according to his own will. - he may not be defeated at that time - his device to enter in to the stronghold is sound and not able to be countered.

The king of the north also stands in the glorious land: amongst the orbit of F we have a sub-orbit in GF(8) of the subgroups of the northern octal. (We began with [b,d,f]) and we ensured by GF(p, 6n) that there is also a short orbit of length r = |f*| / 7. When the octal {a,b,c,d,e,f,g}0 falls, there is both a short orbit in F* restricted to all the subgroups of GF(8) , (but also a short orbit of GF(8) in F by generators turned back on their ranks seven times.) Thus the king "stands" in the glorious land.

In this manner by the hand of the king of the north, he enters into the fortress of the south and also the whole octal's subgroups - which by the effect of the "ramp" in the orbit is consumed completely as part of his total forces.

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