A New Earth

We see the description of the habitation of the saints, in the new Jerusalem that fills the "earthy" elements about the throne. The city is enough to satisfy God as salvation "filled" - as "enough"; as well as being symmetrical for the saints to live and reign with Christ in freedom forever.

-- Click To Expand/Collapse Bible Verses -- Rev ch21v9-27
Rev 21:9 And there came unto me one of the seven angels which had the seven vials full of the seven last plagues, and talked with me, saying, Come hither, I will shew thee the bride, the Lamb’s wife.
Rev 21:10 And he carried me away in the spirit to a great and high mountain, and shewed me that great city, the holy Jerusalem, descending out of heaven from God,
Rev 21:11 Having the glory of God: and her light was like unto a stone most precious, even like a jasper stone, clear as crystal;
Rev 21:12 And had a wall great and high, and had twelve gates, and at the gates twelve angels, and names written thereon, which are the names of the twelve tribes of the children of Israel:
Rev 21:13 On the east three gates; on the north three gates; on the south three gates; and on the west three gates.
Rev 21:14 And the wall of the city had twelve foundations, and in them the names of the twelve apostles of the Lamb.
Rev 21:15 And he that talked with me had a golden reed to measure the city, and the gates thereof, and the wall thereof.
Rev 21:16 And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal.
Rev 21:17 And he measured the wall thereof, an hundred and forty and four cubits, according to the measure of a man, that is, of the angel.
Rev 21:18 And the building of the wall of it was of jasper: and the city was pure gold, like unto clear glass.
Rev 21:19 And the foundations of the wall of the city were garnished with all manner of precious stones. The first foundation was jasper; the second, sapphire; the third, a chalcedony; the fourth, an emerald;
Rev 21:20 The fifth, sardonyx; the sixth, sardius; the seventh, chrysolite; the eighth, beryl; the ninth, a topaz; the tenth, a chrysoprasus; the eleventh, a jacinth; the twelfth, an amethyst.
Rev 21:21 And the twelve gates were twelve pearls; every several gate was of one pearl: and the street of the city was pure gold, as it were transparent glass.
Rev 21:22 And I saw no temple therein: for the Lord God Almighty and the Lamb are the temple of it.
Rev 21:23 And the city had no need of the sun, neither of the moon, to shine in it: for the glory of God did lighten it, and the Lamb is the light thereof.
Rev 21:24 And the nations of them which are saved shall walk in the light of it: and the kings of the earth do bring their glory and honour into it.
Rev 21:25 And the gates of it shall not be shut at all by day: for there shall be no night there.
Rev 21:26 And they shall bring the glory and honour of the nations into it.
Rev 21:27 And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb’s book of life. (KJV)

The dwelling place of men when with God is within Christ. We expect to see an equivocation of the cosets of K4 in the octal with those elements in the K4 ultrafilter that contains the octal.

We are well aware that the K4 subgroups spanning the octal fall into groups of three (all containing some element (say "a") as an intersection) - these groups themselves form a K4 group.

i.e.: [0,a,b,c],[0,a,d,e],[0,a,f,g] all form a subgroup taking the complement of the symmetric difference in the octal.

As equivalent to a specific K4 subgroup of the octal we are forced to merely keep the correspondence to a single element if we restrict ourselves to the right hand. i.e., [0,a,b,c] as a subgroup of [0,a,b,c,d,e,f,g] forces us to use a=1 and then to reject the group [0,a,b,c] as potentially "static" under the frobenius map on GF(8). (we can not have b<=>c under frobenius). Thus we must cut off two parts if we consider the GF(8) frobenius map as multiplication on GF(4).

The solution then is to use the left hand subgroups formed by their complements in the octal (with unity corresponding to fixed subgroups under frobenius in the octal.

so if (a=1) then [0,b,d,f] is fixed by frobenius on the seven cycle (a,b,d,c,f,g,e). Its complement [0,a,c,g] is then generating a second octal in the same seven symbols.

If we choose groups of K4 subgroups as before but from this alternate set of complement groups generated by the one seven cycle, then we apparently "shift" unity and take the complements of the original groups so in each case unity corresponds under the seven cycle to the remaining elements in two octals.

i.e.: (a,b,d,c,f,g,e) corresponds to a fixed group under frobenius of [0,b,d,f] with a = 1. Then, in correspondence between right and left hands,

Now conversely, if we take our groups of subgroups as from the right column shown here, then if a=1 then the group of subgroups [0,a,e,f],[0,a,b,g],[0,a,c,d] in the left-handed octal that corresponds to the fixed group [0,b,d,f] (in our "sun" or right handed octal under frobenius)

Our K4 ultrafilter sat at the right hand or sun octal, (from the middle column) as a static group a = (b,d,f) preserves the desired K4 operations as found in the left-handed octal as with the "bow" inducing multiplication of C3 over a K4 group of subgroups (induced of frobenius on GF(8)) in the right hand octal (of the middle column shown). And it does it in a familiar way so as to preserve the octal ultrafilter without having two parts "cut off".

Pretty deep stuff, but no one said it would be easy.

Aside from the imagery of the purity and spotlessness of the bride, there are a few descriptions and numbers that jump out straight away. Firstly the wall is stated to be very high - that is unmovable or unassailable. As this new city is as a new spotless coset of K4 for the dwelling place of men in the rest of Christ - As corresponding to a complement subgroup and an element under the seven cycle. Because the complement octal is set under every seven cycle acting on the right hand octal - and is always the same; we see that we have four choices of unity from each K4 coset under each seven cycle.

We also know that in Christ there are three automorphisms of the Field GF(8) with four choices of fixed subgroups in the octals (3x4=12) - but there are actually eight C7 groups for a properly fixed subgroup for each choice of unity. (3x8=24) However in the K4 ultrafilter we have 12 possibilities - four choices of unity in the octal and three automorphisms to form the multiplicative group in GF(4).

So we have plenty of factors to make the number 12 relevant. The "Earthly" three elements aside from unity corresponding to the right hand K4 subgroup contain the "full octal" as groups of subgroups and there are four choices of unity for each static subgroup. There is then "four high unassailable walls" (it is not possible to be separated from the love of God as to become outside of this "rest" state of unity and the static group, i.e. to become numbered as 666.) There are three automorphisms of the Galois group over GF(8), corresponding to the three groups in operation in our GF(4) of K4 groups, giving us "three gates" on each wall comprised of three rest states in Christ.

Each rest state is as a floating unity comprised of groups in the left or right hand and corresponding to single elements "as slain" which is their intersection of their K4 forms. The 144,000 is selected from those in those rest states and are equivalent to selection from a set of twelve "tribes" corresponding to those rest states of the K4 ultrafilter over that of the octal - which has four states in the octal that justify its three elements, giving us 12 "tribes" in rest states.

The foundations of the city have the twelve names of the apostles signifying that this is indeed the "New Earth" as mentioned in the previous page of this section: The twelve gates have the names of the tribes of Israel because Jesus IS the God of Israel revealed in the old testament. The law is His law and as Christ said, The Son of Man is also Lord of the sabbath. Those that enter in are taken "From the lost sheep of the house of Israel". (i.e. The remnant.) The jewels conversely show in analogy that there are twelve places filled, as if from the parable as guests brought into a wedding from the streets, rather than those originally bidden. Christ chose us, not we Him.

The city is described as foursquare and being equal in its dimensions of length breadth and height, as equal in symmetry with respect to its gates and foundation - that they are describing the same rest in Christ. There are three gates on each wall corresponding to the three elements of the K4 ultrafilter: and the walls themselves are divided by the gates into a 4x4 grid in a square or symmetrical pattern, (foursquare). The replacement for the system of the four horsemen of the old earth is completely and symmetrically filled rather by the kingdom of God - there is no remnant of the old left behind.

When the city is measured it measures as 12,000 furlongs and the wall 144 cubits The length, breadth and height are equal,. (The three vectors or dimensions of the K4 or as the GF(8) ultrafilter(s)) and the difference shown in the city now is a multiple of 12 - with the factor of 1000 shows the rest within the city is to those that enter into the city through the twelve gates with the fellowship of God, and the wall that measures 144 cubits also shows that those that enter in are only those that have the seal of the living God in their foreheads. (According to the measure of a man, or "one" man of the 144 rest-states, not as the measure of God, which is patient with a factor of a thousand.)

The richness and purity of the description of this new Jerusalem is befitting the dwelling place of God, but the clarity of the glass, the purity of the Gold and the wealth of the foundation of the city are more important - There can be nothing less than a perfect gift to His Son that is found in His bride. We see the richness of the righteousness in Christ as shown through these descriptions of His majesty - not as a "storehouse" of coins and jewels, but of the greatness of God.

The end of the chapter puts us back on the more familiar ground of a description that the city will be filled with those whom keep the gospel of God. There is no sun or moon to light the city - Jesus is the light thereof: We see the light is given by the K4 ultrafilter, not as the lamb slain: but as containing C7 and the octal as two of its three elements. There is no temple, but God dwells amongst the children of God, His people.

Continue To Next Page

Return To Section Start