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#75 Correspondence between the inner Tree of Life and the 3-d Sri Yantra

Although traditionally regarded as a triangle, the downward-pointing, three-sided figure at the centre of the 2-dimensional Sri Yantra is not, from a strict, mathematical point of view, a triangular area that can be turned into a Type A triangle. This is because the bindu as a separate dot or point symbolising the Absolute is assigned to its centre. As the source of Creation, the Absolute (Parabrahman) stands, so to speak, 'outside' it always, so that the bindu cannot be counted with other yods or included with all the geometrical components of the Sri Yantra, which represents God's Creation. For this reason, it is illegitimate to treat this central, three-sided figure as a true triangle on the same par as the 42 triangles that surround it. It is, however, legitimate to do so when the Sri Yantra is a 3-dimensional stack of four sheets of Type A triangles because, then, the central bindu* hovers above the central (white) Type A triangle. In this case, 15 turquoice yods in the latter other than corners surround its centre. Each Type A triangle contains 19 yods, that is, 16 yods other than its corners. The number of black yods other than corners in the 42 Type A triangles = 16×42 = 672. The number of yods other than corners of the 43 Type A triangles that surround the central axis passing through the bindu and the centre of the central triangle = 15 + 672 = 687. Remarkably, this is the number of yods in the seven enfolded polygons of the inner Tree of Life when their 47 sectors are Type A triangles**:

 Each set of the 7 enfolded Type B polygons has 687 yods. They comprise 15 black yods (two yods on the root edge, seven centres & six other yods on the vertical, internal sides of the sectors of the hexagon shared with the Tree of Life) and 672 coloured yods. The centre of the 3-d Sri Yantra is surrounded by 687 yods in the 43 Type A triangles that are not their corners. They comprise 15 turquoice yods in the central triangle and 672 black yods in the 42 triangles surrounding it.

Furthermore, these 687 yods comprise 15 black yods, namely, two yods on the root edge that are associated with the other set of enfolded polygons, seven centres of polygons and six more yods on the vertical, internal sides of the hexagon that are shared with triangles in the outer Tree of Life because they line either its Pillar of Judgement or its Pillar of Mercy, as well as 672 unshared, coloured yods that surround the seven centres. In the inner Tree of Life, this 15:672 division differentiates between those yods that are either associated with the other set of polygons or shared with the outer Tree of Life and those yods that are intrinsic to the inner Tree of Life and surround centres of polygons. In the 3-dimensional Sri Yantra, this division distinguishes between the yods that make up the central triangle symbolising the trimûrti of Shiva, Vishnu & Brahma and the yods that belong to the 42 triangles surrounding the central one. What more convincing evidence of the equivalence of two sacred geometries could be offered? It is ridiculous to ascribe this matching to chance because consistency then demands that all other examples of correspondences between the Sri Yantra and sacred geometries discussed elsewhere in this website must be regarded, likewise, as coincidental — the probability of which is extremely small, making it highly implausible that they could all be due to chance. The two yod populations are the same for the simple reason that the two sacred geometries are isomorphic representations of the same thing — namely, the 421 polytope (see 4-d sacred geometries), whose 240 vertices determine the symmetry group E8 governing the E8×E8 heterotic superstring forces that build the universe. Being isomorphic, they embody the same parameters characteristic of holistic systems, such as this superstring. It is shown in 4-d sacred geometries that the inner form of 10 overlapping Trees of Life is the 421 polytope representing these forces, whilst their outer form is the UPA/subquark state of the E8×E8 heterotic superstring. What is being revealed here are two versions of the same cosmic blueprint, which — being isomorphic — embody the same, universal parameters of holistic systems.

As

153 − 15 = 3360 = 672×5,

672 = (15315)/5

and

687 = 672 + 15 = (15315)/5 + 15.

This shows how YAH (יה), the shortened Godname of Chokmah with number value 15, prescribes the yod populations of the inner Tree of Life and the 3-dimensional Sri Yantra when both are constructed from Type A triangles. The complete Godname YAHWEH (יהוה) with number value 26 prescribes the number 672 as well because

672 = 4×168 = 22(132−1) = 262 − 4.

This leads to the arithmetic connection between the numbers 15 and 26:

153 = 5(262−1),

or

262 = 1 + 3×152.

The number of yods in a Type B n-gon = 15n + 1. A Type B triangle (n=3) has (1 + 3×15 = 46) yods. Hence, this arithmetic identity has a geometrical expression in terms of a Type B triangle, the centre of which is assigned the integer 1 and whose 45 yods surrounding it are assigned the number 15 of YAH:

Notice that 262 is the number of elements in the 26×26 metric tensor gμν (μ, ν = 0-25) of the 26-dimensional space-time predicted by quantum mechanics for spinless strings. The Type B triangle has 46 yods, where 46 is the human diploid number. Here, therefore, is an arithmetic relation generated by the Pythagorean tetractys between the dimensionality of this space-time and the number of chromosomes in the nucleus of the human cell. There are four elements in the diagonal of the 4×4 metric tensor ημν of 4-dimensional, Minkowski space-time that became the corner-stone of Einstein's Special Relativity. They are: −1, 1, 1 & 1. Hence, 672 (=262−4) is the number of metric tensor elements in 26-dimensional space-time other than these four elements, which are the only non-zero elements of ημν. They comprise (26−4=22) diagonal elements and (672−22=650=65×10) off-diagonal elements, where 65 is the number value of ADONAI, the Godname of Malkuth. This Godname is used by Jews as a substitute for YAHWEH, "the Ineffable Name of God," whenever they recite their scriptures.

* The bindu is omitted from the diagram to avoid creating the false impression that it is meant to be counted with all the other yods.

** For proof, see #72 at Wonders of correspondences.

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