# 82 The square as a representation of the inner Tree of Life with its halves joined or separate

 Figure A
Consider a 23×23 square array of 529 dots. They comprise four brown dots at the corners, a white dot at the centre of the array and 524 other dots. The 23 dots lining a diagonal consist of 20 black dots, its central white dot and the two brown dots at its ends. The (529−23=506) dots not on this diagonal comprise two brown corner dots and 504 others (252 red dots in one diagonal half of the square and 252 blue dots in the other half.

As 23² – 1 = 528, the number of dots surrounding the white dot at the centre of the square = 528. Using the formula πD for the circumference of a circle of diameter D and the well-known approximation* of the mathematical constant π as ²²/₇, this is the circumference of a circle whose diameter is 168:

168ײ²/₇ = 24×22 = (23+1)×(23−1) = 23² − 1 = 528.

This number is the gematria number value of Cholem Yesodoth, the Mundane Chakra of Malkuth (see here). The 88 dots on the sides of the square correspond to the length 88 of each of the 6 arcs made by the six corners of a hexagon circumscribed by the circle. The length 84 of each side of the hexagon corresponds to the 84 dots on the sides of the square other than its four corners. Including the central bindu, this number is also the number of points formed by the corners of the 43 triangles in the 3-d Sri Yantra. The four dots made up of the bindu point above the central triangle and the three corners of the latter correspond to the four corners of the square; the 84 corners of the 42 triangles that surround the central one correspond to the 84 other dots on its sides.

The (7+7) enfolded Type A polygons of the inner Tree of Life contain 524 yods. As the two side pillars of the outer Tree of Life coincide with the vertical sides of tetractyses in the two hexagons, the seven black yods that line each side pillar when the outer Tree is constructed from tetractyses are shared with each hexagon. The black centre of each triangle coincides with a hexagonal yod on the side of a tetractys that connects Chesed to Geburah. The 524 yods consist of 16 black yods shared between the outer and inner Trees of Life and (524−16−4=504) unshared yods outside the root edge (252 red yods in the right half of the inner Tree and 252 blue yods in its left half). The following correspondences exist between the 23×23 array and the inner Tree of Life:

524 dots other than corners surround centre → 524 yods in inner Tree;
20 diagonal dots other than corners and the centre of the square → 20 yods either shared or on the root edge.
10 upper diagonal dots other than corners and the centre of the square → 10 yods either shared or in upper half of the root edge;
10 lower diagonal dots other than corners and the centre of the square → 10 yods either shared or in lower half of the root edge.
504 dots other than corners or dots on the diagonal → 504 yods outside root edge that are intrinsic to the inner Tree of Life;
252 dots other than corners outside diagonal in each half of the square array → 252 intrinsic yods outside the root edge in each half of the inner Tree.

These correspondences indicate that a 23×23 square array of dots is an isomorphic representation of the inner form of the Tree of Life. Its arithmetic expression is:

528 = 23² − 1 = 3 + 5 + 7 + ... + 45,

i.e., 528 is the sum of the first 22 odd integers after 1 that can be assigned to the 22 Paths of the outer Tree of Life.

Figure B
If its corners are included, the 528 dots surrounding the centre of the square array correspond to the 528 yods in the separate left-hand and right-hand halves of the inner Tree of Life, each containing 264 yods. The 12 turquoice dots in the upper half of the diagonal of the square correspond to the 12 turquoice yods in the separate right half of the inner Tree of Life that are either on its root edge or shared with the outer form of the Tree. The 12 mauve dots in the lower half of the diagonal correspond to the 12 mauve yods in the separate left half of the inner form of the Tree of Life that are either on its root edge or shared with its outer form. As in Figure A, the remaining 252 red dots in the upper half of the square and the 252 blue dots in its lower half correspond to the 252 yods in the right-hand and left-hand sets of seven enfolded polygons. The counterpart of this 12:252 division in the circle of diameter 168 is its two semi-circles, each of length 264. Each of the three arcs in a semi-circle is of length 88, which is the sum of the length 84 of a side of the circumscribed hexagon and the extra length of 4 that a side has to be stretched and then bent to form the arc associated with it. The length of the three sides of each half of the hexagon is 252, whilst the perimeter of each semi-circle is 264, that is, 12 units longer. This extra length corresponds to the 12 yods either on the root edge or shared between the outer Tree and each half of its inner form. The following correspondences are established:

12 turquoice dots (upper corners or half-diagonal) → 12 turquoice yods either on root edge or shared → extra length of right-hand semi-circle compared with right half of hexagon;
12 mauve dots (lower corners or half-diagonal) → 12 mauve yods either on root edge or shared → extra length of left-hand semi-circle compared with left half of hexagon.

This isomorphism between the circle and the inner Tree of Life runs deeper because the 264 yods in the seven enfolded Type A polygons comprise 41 corners of 47 tetractyses, i.e., 88 corners & hexagonal yods at their centres, and 176 hexagonal yods lining their 88 sides (two per side), i.e., two sets of 88 hexagonal yods, so that they consist of three distinct sets of 88 yods. Each set corresponds to one of the three arcs of length 88 in a semi-circle. The full implications of this connection between the inner Tree of Life and the circle (the basic unit of sacred circular geometries) are explored in the author's forthcoming book "Foundations of Sacred Circular Geometry." Details on how to order it will be posted in the My Books section of this website as soon as the book becomes available.

* As explained in his book (see final paragraph of this page), numerical information about the fundamental nature of the cosmos is encoded in sacred circular geometry in the numbers of circles and their circumferences — not in their exact magnitude but in the integers that they embody when π is approximated by ²²/₇. This restricts the possible diameters of the basic circle appearing in sacred circular geometry to a finite set of integers, of which the number 168 is one. However, it is the only integer that allows exact correspondence between the circumference of this basic circle and the yod population of the inner Tree of Life. In order for the two types of sacred geometry to be equivalent, a basic circle must have a diameter of 168.

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