The Four Beasts

The trumpets may seem complicated, but they are actually a mirror image of the seals. In the seals we equated the four beasts about the throne in heaven with the earthy elements {d,e,f,g} if (a,b,c) is static. The unity element in the seals accumulated across those four upon shifting from one bow in d = [b,d,f] = 1 = {e,f,g} to the remaining three by shifting unity from d to e to f to g.

The trumpets are indeed similar, but the static subgroup is shifted whilst the unity element is held fixed. This may not seem apparent from the previous page but we may start the cycle at any row of each octal: Considering only those four rows in each octal that are not a member of the other three we have our four rows in each, with each octal's four distinct.

a = (b,d,f) = {c,e,g} £
b = (c,d,g) = {a,e,f} £
d = (c,e,f) = {a,b,g} £ start here!
c = (a,f,g) = {b,d,e}
f = (b,e,g) = {a,c,d}
g = (a,f,g) = {b,c,d} £
e = (a,b,c) = {d,f,g}


a = (c,d,g) = {b,e,f} £
c = (b,d,f) = {a,e,g}
d = (b,e,g) = {a,c,f} £
b = (a,f,g) = {c,d,e} £
g = (c,e,f) = {a,b,d} £ start here!
f = (a,d,e) = {b,c,g}
e = (a,b,c) = {d,f,g}


a = (b,e,g) = {c,d,f} £
b = (c,e,f) = {a,d,g} £ start here!
e = (c,d,g) = {a,b,f}
c = (a,f,g) = {b,d,e}
g = (b,d,f) = {a,c,e} £
f = (a,d,e) = {b,c,g}
d = (a,b,c) = {e,f,g} £

and in wormwood'

a = (c,e,f) = {b,d,g} £ start here!
c = (b,d,f) = {a,e,g}
f = (b,e,g) = {a,c,d}
b = (a,d,e) = {c,f,g} £
e = (c,d,g) = {a,b,f}
d = (a,f,g) = {b,c,e} £
g = (a,b,c) = {d,e,f} £

each octal has say "a" = 1 with a different subgroup. Therefore the systems are equivalent to the seals by shifting static subgroup rather than unity, and the same results hold for this system also. Simply put, it just requires me to type more!

Now each row in "£" we associate with the four beasts; but we also equate the devices of satan as being seen to go out from or act within the four beasts; being found in the elements of {a,b,d,g} as in the above "£" symbols. There is in no sense an operation where the wormwood set is an "identity" although it appears to have a "ring of truth" to it. We must in some sense be able to send the wormwood set to {} and obtain our fiat copy of the Klein four group from hurting the oil and wine.

Firstly, we must identify our oil and wine.

Given that we will by construction send the wormwood octal to {} we should note that we must also hold unity fixed. our rows in each "bow" are NOT the rows that hold static the *, # and $ of the previous page. Given that the wormwood correspondence is {}, the octals appear to label naturally to the element of (c,e,f) that they lack. The fourth row that should correspond to the wormwood set or {} is totally absent, we need not look for it: it simply does not exist in all the other three.

The presence of the wormwood octal makes the set of four octals appear to have a commonality of one row from each towards each of the others. We saw this in the seals as each of the four seals shared the same static subgroup. Equally here we may state that the elements {a,b,d,g} correspond to a choice of static triple in the coset of the shared right hand subgroup. The confusion leaves quickly when each of the four octals above is as to pick one of {a,b,d,g} as unity and hold the other three elements as a static triple.

Of course then, there is the appearance of a counterfeit K4 operation when each group's unity element is sent to {}, since these rows do not agree with their correspondences in the other two. for although c = (a,f,g) = {b,d,e} in two of the first three, it is not in the other (but it is in the wormwood) so we have a confusing choice - one of "A vs ¬A". of one of the first three or the wormwood.

Our oil is then the excluded row in the wormwood which we sent to {} and the wine is then the common product remaining, or each octal as the product of the other two. We are however missing the sense that X*X = {} yet again. We must show there is no premise for this at all.

Stating then that our wormwood is "a" which holds fixed {b,d,g} the products are essentially in the other three octals forming as it were [c,e,f] but actually forming [b,d,g] in counterfeit.

There is yet no sense of addition modulo 2. Even when we consider that each of the octals correspond to only one element - not of the subgroup [c,e,f] but in the coset, for they each hold one of {a,b,d,g} fixed as unity with the remainder of the three a static triple. We are confusing the adequate operation of the right hand group [c,e,f] with the cosets of the subgroup. There is no operation outside of the subgroup which is in the original "sun" octal, and not by inference in or across the sea since addition modulo two is not present.

The wine then is not the wormwood group of [c,e,f] that is sent to {} but must be found common to all three remaining octals. This then relates to the wormwood's element from {a,b,d,g} (i.e. "a".)

From top to bottom our four octals correspond to d, g, b and a. To show that "a" is common to the other three it simply states that a = [c,e,f] in the wormwood octal; excluding one always repeats this correspondence of d = [c,e,f], and g = [c,e,f] or b = [c,e,f].

Excluding "a" would lead to the static triple of {b,d,g} or by inference the subgroup [c,e,f]. That the wormwood and trumpet devices converge about this one subgroup does not create an operation in group form over those octals; the device of hurting the oil and wine is deception on a wider scale across the 30 possible octals, yet it is not "well defined" as a binary operation should be.

So, when a seal is opened and a horse is observed amongst the four beasts it shows that a fixed position is not empty, or in truth, not sent to {}. As a result, the rider on the horse shifts from that identity to another, culminating in it's arrival in the pale horse or fourth seal - when the earth is seen to be full of the use of the devices. The trumpets declare that the seals are fully open and the victory is obtained over the enemy: Not only do they declare the divinity and victory of Christ they also show there is no similar counterfeit through dialectic logic (hurting the oil and wine.) The trumpets open and reveal the mystery and declare Christ the only begotten Son of God. In the case of the wider "sea", there is no reason to show that Christ has an enemy with a leg to stand on.

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