The Lord's Bow, The Elders, The Four Beasts

The Lord's bow, or the rainbow is a more generalised form of the mystery of the seven lampstands and the seven stars. The rainbow is the general form; those blessed amongst us that have seen a rainbow from the air may know that they appear to be a closed cricle. In appearance we see seven concentric circles (as seven cycle group elements each from a different group) of seven colours (as it were the seven stars). There are many possibilities for constructing such a bow, the initial two cycles of each row and the "angel" column may be 48 choices for the first and 42 choices for the second. Then there are 2016 such "bows" for each particular octal group. (As there are 30 octals we may expect 60480 instances of bows upon octals, although this number does not occur in the text.) If we include those bows that also generate the elements from a single group, then there are 2304 possible bows on each octal.

There are twenty four elders shown about the throne, these correspond to the eight possible GF(8) fields, each under their three automorphisms by the frobenius map. An automorphism is an isomorphism from one structure onto itself, as if rearranged, but so that the isomorphism conditions hold. The elements 0 and 1 are fixed. These twenty four elders correspond to a single particular choice of unity from the octal group.

The twenty four elders correspond to the 24 possible multiplications and automorphisms upon a single octal group. Without loss of generality in this section this octal is assumed to be the "sun" octal or our reference octal. The "sea of glass" under the throne is revealed to be this set of finite fields (GF(8)). The "sea" refers to the complete set of all 30 octals and their multiplications; (the 24 arrangements form the isomophisms with every C7 group upon an octal) As the throne scene as isomorphic to all in the sea. The "glass" part of the sea denotes "clear" vision everywhere from the throne, or that every octal from the sea "relects" this structure isomorphically. Omnipresence is implied in this isomorphism.

The four beasts correspond to the four elements in the coset of the Klein four group in view in the text. The trinity that dwells bodily in the person of Christ as "sat" at the right hand forms a proper K4 subgroup of the octal. The subgroup in this context is held "static" by the frobenius map and therefore can not contain unity. The remaining four non-zero elements are each represented by a beast of which one beast then corresponds to unity. The six wings on each beast reveal the multiplicative operation (as if flying) from one element to another: There is no multiplicative element required in "flight" to send an element to itself; this being the action of unity.

Addendum
The following was deprecated. (Correction below)

The four beasts each have a face that is one of a "lion", a "calf", a "man" and an "eagle as if flying". A lion is without restraint, a calf carries a burden and a man sins. An eagle is that which carries away a prey, as this eagle is in flight we see the eagle is ready to take it's prey and is "free" to do so. We know from Ezekiel's vision that each beast may be likened to have all four of these faces, but we see in the revelation that these four forms have some homogeneity that allow us to separate them. These identities will occur with the first four seals in greater depth.

Each face then corresponds as a "watch" over the four stages of the dialectic as it accumulates;

Lion - as antichrist - no restraint (one bow)
Calf - lawlessness - a burden (as two bows)
Man - blasphemy - a sin (as three bows)
Eagle - spiritual death (taken as prey) - the wages of sin (as empty set or four bows)

Correction
The "horses of the first four seals" are analogous to the static subgroup of the octal, with the rider as the unity element, (at "rest" which generates the coset within which the three other elements form the "antichrist bow". Here, each element in the coset is represented by a different beast, and instead of there being one "foot" of the horse off the ground (the zero element) there in view is the correspondence of the number of feet "on the ground" of these four quadrupeds!

Eagle (4 limbs up, zero down whilst flying)
Man (3 limbs up, one down whilst walking)
Lion (2 limbs up 2 limbs down whilst rampant, leaping on prey)
Calf (1 limb up, three down whilst walking)

Or possibly, and more likely

Calf (2 limbs up 2 down whilst cantering - hurrying to keep up with mom?)
Lion (1 limb up, three down whilst walking - no rush for the king of beasts.)

So, these four beasts represent in some fashion the number of possible "unity" elements there may be; or rather the number of possible elements that may be reduced to the empty set within dialectic logic. Then, the fixed truth (unity in the field GF(8)) may be ignored while the mind employs the dialectic paradigm.

Whether each beast has four such faces or only the one; The result is the same. The opening of the seals are as a floating unity that unbinds the GF(8) fields to lift restraint on the mental paradigm of the believer (for the unbeliever was always without restraint).

Then, the reference octal (Sun octal) is the one with one face per beast, and upon the earth from the account there is in truth an order to the opening of the seals, but it is given which beast is which: that one of them started first, and the others were subsequent to that in order, to the list of their appearances in the text. Thus I prefer the second possibility above.

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