The Enigma of the figures
According to the Christian Faith, the first angelica hierarchy , that which contemplates and reflects single God in three Persons, includes three choruses: the first associates 7 Seraphes, the second 4 Cherubins, the third 24 Thrones. Why these figures? They individualize, in each angel of each chorus, a different image of God in three Persons.
| Why 7 Seraphes |
Because there are 7 images of the Trinitary God:
three of God in one Person, contemplated by three Seraphes,
three of God in two Persons*, contemplated by three Seraphes,
one of God in three Persons, contemplated by one Seraph.
So, by symbolizing the three Persons by the elements, (1)(2)(3), of one set:
(1) |
(2) | (3) | (23) | (31) | (21) | (123) |
To mean the preeminence of the seventh Seraph, (123), the most similar to God in three Persons, because it reflects the three images in only one set, it should be placed in the center of the circle formed by the 6 other Seraphes, on the throne of the biblical theophanies probable seat, before its fall, of Lucifer.
* Cf, the Dogma of Circumincession, according to which each of the three Persons sits in each of both others.
Why 4 Cherubins Because there are 4 images of God in three Persons, While indicating by (1) (2) (3) three Persons,
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These 4 Cherubins are four images, different, of God in three Persons, because they recapitulate the three Persons in four different ways.
John Ap 4.6 saw 4 Cherubins - said Animals or Alive according to translators - “in the middle of the throne or around the throne.” Indeed, the fourth Cherubin is the image, (123), of the seventh Seraph and, for this reason, can appear on the central throne.
(1)(23) |
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(123) |
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(2)(31) |
(3)(12) | |
Although different four Cherubins, as images of God, are equal and, for this reason, must, each one, to get the capacity to replace each of the three others - i.e. to permute - so that all four contemplate God in equal ways.
The behavior of Cherubins and that of the angels of the third chorus, Thrones, cannot be described separately.
Why 24 Thrones |
So, the number of the permutations, i.e. arrangements which 4 objects can take, is 24. But, here, the nature of four Cherubins makes that their 24 permutations could be the sum of the 6 permutations of their four faces described by Ezechiel and John.
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Ezechiel and also John, briefer, give a further information very important, often difficult to interpret, on the nature and the movement of Cherubins and the Thrones.
Cherubin comes from a Semitic word, cherub, which indicates fantastic beings. Indeed, Ezechiel describes biblical Cherubins like fabulous creatures, equipped each of four faces: one of man, three of animals.
If the definition given higher of four Cherubins - four images of God in three Persons: (1) (23) (2) (31) (3) (21) (123) - is founded, then the four strange faces described by Ezechiel symbolize them, although it is random to allot to each one the corresponding divine image.
This figuration, biblical, becomes less hermetic if it is visualized geometrically by the regular tetrahedron, whose Plato said that it was simplest of volumes.
It is about the geometrical representation of the mathematical group G4 which is the set of the permutations of 4 objects.
In this model, to the four faces of Cherubin the four faces of a tetrahedron correspond and, since there are four Cherubins, four tetrahedrons symbolize them.
Like that of 4 objects, the permutation of the 4 tetrahedrons, and thus that of 4 Cherubins, gives, account not held their faces, 24 arrangements. But starting from each tetrahedron, and thus of each Cherubin, one can visualize another form of permutation, by regarding the tetrahedron as a triangular pyramid which the three faces and the base are equal triangles,
Since each Cherubin was defined like an image of God in three Persons, those must be able to be localised on the pyramid which represents Cherubin.
For this purpose, each face of the triangular pyramid symbolizes one of the three Persons: (1) (2) (3), while its base appears all three Person: (123).
6 rotations, sinistrorsum or dextrorsum, of the three faces of the pyramid symbolize the 6 permutations of the three Persons, who constitute six arrangements:
(1)(2)(3) (1)(3)(2) (2)(3)(1) (2)(1)(3) (3)(2)(1) (3)(1)(2)
Each of four Cherubins carries out the six same permutations which are thus, in accordance with the biblical revelation, 24, (6 X 4).
To each rotation of the pyramid, its base, (123), turns, carrying out solitairement the permutation known as identical by which it replaces itself, by indefinitely reproducing its image of God in three Persons.
Each Cherubin is made by one of the three Persons and his complement: the two other Persons, with whom they constitute a set of three Persons. Fourth Cherubin: does (123) get, itself also, a complement?
Already image of God in three Persons: (123), that it contemplates in the Seraph which carries it, fourth Cherubin thus does not seem to need, however the Set theory allots one, very unexpected of them to him: the empty set.
This empty set belongs to the eight subsets of any set of three elements. To describe it here it is necessary, initially, to refer to the list of the Seraphes already proposed:
(1) (2) (3) (12) (23) (31) (123)
Mathematically, it would be the list of the subsets of a set of three elements: (123), if it did not miss the eighth subset, the empty set: Ø.
The empty set is zero, nor “nothing”. A bag containing of the objects could popularize it. Indicated here by brackets: (), but more often symbolized by accodances: {} or itself: Ø, it is the container of the unit of which, for this reason, it is the complement.
Elements: 123 are the contents of the unit, (123) is the contents of the set in its container, its complementary brackets.
The empty set, containing of the set of the angelical choruses , is logically the Sky of the Bible, often quoted like habitat, never like inhabitant.
Why the set does part of its subsets? Because it is a mathematical asset: any unit is subset of itself. As a principle of its subsets, he is written between accodances: {123}, as a member of its subsets, it is written between brackets: (123).
Thus, the chorus of the Seraphes, as that of Cherubins who contemplates them and that of the Thrones which contemplate Cherubins, it is composed by the subsets of an original unit of three elements {123}.
This original unit is the image of the three Persons of the Trinity, whose vision would be the divine source of the biblical cascade of the angelical hierarchies .
Do you think that the mystery of the Holy Trinity - Only one God in three Persons, of which Each one is God - gave the key of the Enigma of the Figures, in shining their common origin and the logic of their relations?
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The Christian doctrines proscribe the introduction of a mathematical composition as a God. The figures which precede make exception to this rule, because they are the base, revealed, of the Christian Faith: 1 only God in 3 Persons, origin of the continuation: 7 Seraphes, 4 Cherubins, 24 Thrones.