The Strength Of The Kingdom

Moving swiftly on,

We stated that the field F was of order 2⁶ⁿ The smallest such field is of order 64, yet n may be any positive integer. The king of the north is now extending this field of many ranks (cosets of GF(4) in F*) to encompass his whole people. His "upright ones" may be assumed to be those elements in all the ranks that equate to unity -and not those in the centre (namely the powers of the generator acting on unity in the octal).

Now the unity is found in the ranks of the king of the north, at some b_i, d_i, f_i etc. In order to make the attempt to establish the vision of manufacturing a set of ranks of GF(8) rather than cosets of GF(8) in F*, the inter marriage of these unity elements in his ranks with the elements in the centre (the daughter of women) is made.

We may assume that the southern women were given as spoil to the northern "upright ones" in order to close the gap between unity and the desire to place unity only in the centre, and make a mapping from unity on to some power of the generator producing the ranks. Such a mapping does not exist (I know, I’ve tried it!)

She, will not stand on his side, (she will remain a "southerner") neither be for him (this act will not strengthen the north - a failed manoeuvre). That the "daughter of women" is given shows that in the phrase "corrupting her", we have that her proper place is in her power of a generator she has already! Adding in the map simply makes a mess of all the elements in their ranks, they are "shuffled", or reordered, but that’s it. The vision itself fails.

The next attempt to realise this vision of the structure of the trinity in terms of military forces takes place with the king of the north looking to the isles, (coasts.) He looks to the borders of the orbit of his ranks to try to fix the effect of the ramp at the ends of the orbit of GF(4) itself.

A prince - i.e. a rank, steps up to put an end upon this slaughter (taking many) of those that are clearly unable to prevent this ramping at the end of the orbit under the generator. The prince has the same set {b,d,f} but under the effect of the ramp ordered say to {f,b,d}. He causes the effect of the ramp to cease by simply having the orbit shortened and cycled upon himself. (The orbit is shortened from |F*| to m = |F*| / 3)

The prince is not part of those that are "extraneous" in the orbit, but himself as a reordering of the "king's own triple" He does so by reordering the field. This may be done with frobenius as if cycling a field GF(4) upon the prince's K4 subgroup, say with x->x^2²ⁿ. In this fashion, the reproach (ramp effect preventing the vision) is caused to cease for the behalf of both the king and the prince (which are the same set {b,d,f}) without the prince being in an extraneous part of the orbit - and is done so that the reproach is turned or "twisted" or "restructured" upon him.

After this the king turns to the fort of his own land, say [b,d,f] as before. Now, the ramping effect ceased of the prince in GF(p, 6n) acting upon the unique subfield GF(4) of that extension (which can not be [b,d,f]) is held fixed by the map x->x^2²ⁿ because GF(4) is of degree 2, and 2n is clearly even.

Yet, the fort of his own land refers but to the octal as it began, [b,d,f], a = 1, {c,e,g} as before. The king tries to alleviate the effect of the ramping upon the subfield GF(8) of F also. This would require a second map x->x^2³ⁿ. Now, this holds fixed the subfield GF(8) but not the subfield GF(4), as GF(4) is not a subfield of GF(8). But now, all subgroups of the original octal are fixed!

He stumbles that now the fort of his own country is fixed (there is now no unique static subgroup); he falls because he tries to make a similar change to the fort (the static subgroup) within his own land: Failing by trying to undo the ramping of K4 subgroups of GF(8) in order to find some similar separation between his fortress as GF(4) and the groups in GF(8), separating them as Field and cosests (ring ideals) to make a morphism and set him up as god himself. (Christ is not reprodiced - as sat at the right hand of God, Christ is the one in whom the whole trinity dwells bodily. (Father and Spirit are within him. - He is not merely a subgroup.)

Why should such an effort fail? well the account was attempting to find a solution in numbers, that extending into extensions GF(p, 6n) having some small success with applying frobenius at the end of every cycle of a short orbit for both GF(4) and GF(8), there is no common solution that holds one fixed inside the other - there is no combination where GF(4) is a subfield of GF(8) in any extension. The closest that may be constructed are extensions of GF(2, 6) to remove the ramping to them; but this is not that which was desired.

He stumbles, falls, and is not found - his vision to make himself God fails completely.

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