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Revelation
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 The Throne Of God Beginning with the octal group we may note that the group C7 may act as multiplication to give us a Galois field of eight elements. We also note that the K4 subgroups of the octal are preserved by seven cycles from 8 groups (isomorphic as C7). We may also define addition on the K4 subgroups by taking the product to be the complement in the octal of their symmetric difference. Thus (0,a,b,c) + (0,a,d,e) = (0,a,b,c,d,e,f,g) - (b,c,d,e) = (0,a,f,g) Then we see how the whole octal also acts as the multiplicative identity zero. The octal "Sits as enthroned before the seven lamps of the Holy Spirit" We write this operation as "K4 subgroup addition" or (A v B)^c equivalently. (0,a,b,c) + (0,a,b,c,d,e,f,g) = (0,a,b,c,d,e,f,g) - (d,e,f,g) = (0,a,b,c). Likewise the eight C7 groups form with one C7 group acting as "The angel" (as in the mystery of the seven churches) form the rainbow about the throne, (c.f. compare the "churches" with colours in "the rainbow"). The eight possible C7 groups that form with the same octal a field (GF(8)), each have three automorphisms by frobenius: Thus there are 24 arrangements of the same underlying (additive) octal, the elements of these 24 arrangements are analogous to the 24 thrones for the elders enthroned about God. As the Father, the additive octal is constant here, whereas the "rest" in the Spirit associated with this particular arrangement, (We will consider one element as unity for now, say "a"=1) is valid for each one particular choice of identity. The set complements of the K4 subgroups of the "Father" (or octal) say, {d,e,f,g} are cycled under the seven cycles of the Holy Spirit also. They have "six wings" as well as the action of identity or rest - which is important also. They are also "The four beasts" about the throne and are analogous to "The earth" wherever it is mentioned in the book of revelation. Under the action of frobenius, There is a fixed K4 subgroup,.. and since unity must not be an element of this subgroup we see that one of the four beasts must be associated with unity, and the other three are then cycled amongst themselves. We can define a similar octal from the action of the currently applied seven cycle to these three non-unital beasts and define a K4 subgroup of the internal product as before. I.e. if we start with {a,b,c,d,e,f,g} with a = 1 then under (a,b,d,c,f,g,e) as a seven cycle we can make the associations; a = (b,d,f) or (c,e,g) Where the seven cycle is applied to each row to result in the next. Then our second octal is defined by the elements in the rightmost column, so that c = e + g etc. Counter intuitively we will use our original octal as the "right hand of God" and the subsequently calculated octal formed by our new triples as the "left hand of God." We will also refer to the octals as "right handed" or "left handed" similarly. In each case The Holy Spirit is taken to apply to both whenever they are mentioned together,.. there will be no mention of a "left handed element of C7". What of other octals in seven symbols? Some effort may be required to write them all out but there are 30 different octals in seven symbols (isomorphic to each other). A triple of elements appears in six different octals as a subgroup, and each C7 group acts on only two octals. The resultant left handed octal may be different only if there is a different association of unity to the static K4 subgroup. (And that requires a different seven cycle.) The 30 octals are analogous to the "sea" wherever it is mentioned. It may be also noted that concepts of time in revelation are related to the octal groups. One may have noticed that there are 24 elders and 24 hours in a day, there are 30 octals or possibly assigned values of the seven symbols (each a month) and then the whole seven cycle itself which represents a year (albeit with seven months.) The sea of glass mentioned in the text no doubt refers to the full set of 30 isomorphic octals,..shown clearly present in the throne scene here. Glass being the term analogous to transparent or visible. Although most of revelation is concerned with the primary or "sun" octal, its isomorphic copies in the other octals in the sea are present throughout revelation, as the movement from one octal into another is equivalent to a transition away from or out of God's (sabbath rest) grace and obedience to God. The "stars" that are not visible as the sun is (during the "day") are referred to in the text, as is the moon which is a transitional state from one octal, (usually the "sun") of day towards another octal of "night". The "stars" refers to this wider set of other octals in the sea, rather than the primary "sun" which is equivalent to the throne of God. |
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