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Three Bags, Full of What?

I do hope you carefully read through the previous page "Tested Whilst Surprised". you may find it very helpful to open that page in a new window and have this page alongside it in a split screen format. I have never read a coherent account spoken or read one on precisely the nature, or meaning of Ezekiel's vision. I have my own of course. Remember you read it here first! 

Well, if you didn't see it coming, since this is a "maths" section, and we have defined the elements of the Galois Field of eight elements as not only the seven-cycles of the multiplicative group and those non-zero elements of the additive group (0,a,b,c,d,e,f,g), but also the elements of the additive group as the subgroups (0,a,b,c), (0,a,d,e) etc. which are cycled by the appropriate individual elements of GF(8)*.

So how do we add these subgroups together?

We define the symmetric difference of two sets as all of those elements of either set not common to both. I.e. (S ∪ T) - (S ∩ T) using union and intersection as one would have learned in school. Also, we need the "set complement" which is basically taking the elements not present in a subset from the total set of elements, and making a set of them as a result. E.g. if the set-space is {a,b,c,d}, and S={a,c} then the complement of S is {b,d}.

So using the notation A v B as the symmetric difference of A and B, and Sc as the complement of S, we define the operation of addition on our additive subgroups as...

G + H = (G v H)c

So; (0,a,b,c) + (0,b,d,f) = (a,c,d,f)c = (0,b,e,g) and likewise for all seven subgroups and the combinations.

But wait!   (0,a,b,c) + (0,a,b,c) = {?}c = (0,a,b,c,d,e,f,g), supposedly the additive identity, zero. - Which is not a problem, since without loss of generality it is indeed well defined.
(0,a,b,c,d,e,f,g) + (0,c,e,f) = (0,c,e,f).
Multiplicatively, the seven-cycles merely permute the elements of our 'zero' here, and the set of elements does not change up to a reordering.


The book of Revelation, in it's reference to the seven spirits of God mentions them as "seven lamps of fire..." before the throne, and one sat on the throne with a book of seven seals. There are four beasts described, and the vision goes on to reveal that Jesus Christ, the one with the seven stars in his right hand, and walks amidst the seven candlesticks takes the book and one by one opens the seals.

The four beasts are present with the lamb, or better put, to the Jesus 4-group (for instance {0,a,b,c}) they are the remaining elements {d,e,f,g} There are seven distinct subsets, complements of the 4-groups that are also cycled by the multiplicative elements.

The seven stars, (angels) and the seven candlesticks (churches) are interesting. The messenger to the churches carried the book to seven churches in Asia Minor, could the stars be multiplicative elements, and the churches as additive subgroups?

The book is most likely the "Lamb's Book of Life", The seven seals on the book would indicate that as far as the work of salvation goes, things are not finished. The rainbow around the throne is definitely symbolic of the covenant that God made with Noah after the flood waters had abated. The "marriage" of the seven churches to the names written in book of life once the seals are broken will become a one to one correspondence.

The Lamb is envisioned as having seven horns and seven eyes, which are the seven spirits of God. There are three non-zero (zero being outward looking) elements. Seven additive, seven multiplicative, technically two sides of the same Father. My guess is the eyes are the Holy Spirit.

The upshot is that Angels, Churches, Holy Spirit, Father, Christ, through the opening of the book of life, will become through Christ equivalent through a regression and congruence of these like-element additive subgroups. The depth of these regressions is a little hard to guess, but I can guess it may cycle, or it may be infinite whilst the Godhead is finite (Ultrafilter). I am in no way saying man will be god, or there are many Christs. That is totally non-biblical, and there is nothing to pan it out.

The other thing to glean about this is the four beasts, which have "eyes before and behind" That they look out as well as inward means that they are separate from Christ the lamb, They 'contain' the kingdom of Heaven. They are a representation of reality. They are part of the inward looking Father, but the outward looking Christ. Perhaps, the "left hand of God", as opposed to Christ who is at his Right hand. That "zero" is the whole thing, if to be "in" Christ is to be saved and everything has to be "in" God, that God looks one way or the other and views the same thing is not a surprise at all. The solution is how everything is divided up, in it's structure.


Explanation of Ezekiel's Vision

Not to overstate the obvious, but Ezekiel is an Old-Testament Prophet. That is, Ezekiel lived before the commonly accepted time of Jesus'  life on Earth pinpointed by the years in which he could call someone "Mother" and not be misunderstood. It is no surprise that there is no mention of the seven Spirits of God, or of the Lamb. Jesus Christ's affirmation of the new covenant had not occurred, and there was no requirement of Israel to acknowledge Christ for their salvation. He is yet to be revealed to them at this point. (Some were such entrenched Israelites, they didn't recognise him when he arrived!)

The main difference between Ezekiel's cherubim and the four beasts about the Throne of God in Revelation is that the former have four wings, and the latter six.

Imagine for a moment the complements of the four-groups in the Octal group GF(8)+, and only them. Then imagine the strange behaviour that they cycle with the action of GF(8)*, Then, imagine them as sets of four 4-groups, or four complements of four 4-groups.

The wheel within a wheel becomes the cycling of these four complements, remaining within themselves by regress four complements each. Each four cycling four. The overall effect and Ezekiel's description seem to match. - Think of a kaleidoscope.

The "rings" are the extremity of the wheels, and are the boundary that is filled by Christ. The firmament has the Father in the sense of "looking out" as above. There are many mighty signs of God's power; the appearance as of fire, thunderings and lightenings. Most conspicuously, there again is the presence of the rainbow. I am put in mind of the book of Zechariah, in which there is the following.

Zec 2:4 And said unto him, Run, speak to this young man, saying, Jerusalem shall be inhabited as towns without walls for the multitude of men and cattle therein:
Zec 2:5 For I, saith the LORD, will be unto her a wall of fire round about, and will be the glory in the midst of her.

That each Cherubim has two 'missing' wings implies there is a dimension of travel not visible to Ezekiel. I do not expect this is the movement of 4-subgroups congruent to the elements in the complement sets. I believe simply that the operation of addition (G v H)c when applied to two of the complement sets gives the same result as would their complement 4-groups. This result being a representation of Christ, I wouldn't expect them to appear in the vision because the operation is not closed on the set of complements. (Neither can we add types in like manner, group with complement, as we produce the empty set.) However, since the Father is as an element in Christ, addition for the whole of GF(8) includes this extra "dimension" for the four beasts, again preserving the "eyes within and without" as indeed the 4-group is a subgroup of the Octal.

Ezekiel's life was one in troubled times in exile with the rest of Israel in Babylon. The opening chapters of the book describe the rebellious nature of the exiled nation and God sends Ezekiel after the vision with the promise they will know he is a prophet among them. That the vision is "without" is no surprise. God has a big stick and is willing not just to wave it but bring it crashing down. The message that they are erring in their ways and have left God's camp is a far better explanation of the vision than one which equates it to a representation of the old covenant. There is no "empty offer" of the old covenant.

Israel is now spiritual in Christ, not a result of bloodline, but of adoption. What is hard for some to believe, is not that everyone sins or will sin and needs forgiveness, - but that if there was a person who had never ever sinned, yet did not believe Jesus is Lord: He would not be saved at all. He who has not the Son has not the Father. In or out is a consequence of belief. Some may indeed be his children and yet make God want to physically retch. (Letter to the angel of the church of the Laodiceans - Rev 3:16)

It could follow therefore that one could be perfect, but such an asshole that you won't get in to heaven. If God just doesn't like you - Tough! It's a hard saying, that our good deeds are as filthy rags, and we may have great faith in (a) God, even (a) Gospel. If it isn't THE GOD, and THE GOSPEL, then you have no JESUS. there's no (a) Jesus to fit the former other.


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