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#25 The first (4+4) enfolded Type B polygons embody the number 474 of Daath
Article 48 (p. 10) shows that the first (4+4) enfolded Type B polygons of the inner Tree of Life constitute a holistic system with 490 (=49×10) yods, where 49 is the number value of El ChAI, the Godname of Yesod (see #18 for how this Godname prescribes the inner Tree of Life). It means that certain parameters quantify their properties that are found also in other sacred geometries. As now shown, they also embody the gematria number 474 (see table here) of Daath (דעת, "knowledge"), which is the non-Sephirah located below Chokmah and Binah but above Chesed and Geburah (see diagram here).
When the outer Tree of Life constructed from Type A triangles is superimposed on its inner form composed of (7+7) enfolded, Type B polygons, certain yods are shared between them. They are (see diagram):
1. the seven red yods on the two Paths on the left-hand Pillar of Judgement, which are sides of tetractyses in the left-hand hexagon;
2. the seven red yods on the two Paths on the right-hand Pillar of Mercy, which are sides of tetractyses in the right-hand hexagon;
3. the red yods at the centres of the two enfolded Type B triangles, which coincide with the two hexagonal yods on the Path that connects Chesed and Geburah and which lies in the plane containing the two side pillars.
Each set of seven enfolded polygons, therefore, shares eight red yods with the 16 tetractyses making up the outer Tree of Life (this remains true whether the polygons are Type A, Type B, etc). The number of yods intrinsic to the first (4+4) enfolded, Type B polygons = 490 − 8 − 8 = 474, which is the number of Daath.
When they are Type A, the first four enfolded polygons contain 90 yods outside their shared root edge. This indicates their holistic character, for the sum of the 10 integers in the Lambda Tetractys is 90 (see here). As eight of these yods are also yods of the outer Tree of Life, the first four enfolded, Type A polygons have (90−8=82) yods outside the root edge that are intrinsic to them. Of these, 13 yods outside the root edge belong to the triangle and 20 yods outside the root edge surround the centre of the square. Hence, the number of yods in the two enfolded, Type A triangles & the two enfolded, Type A squares that surround their centres = 4 + 2×(13+20) = 70. This is the value of the Hebrew letter ayin (ע) in the word 'Daath'. There remain four centres of the two squares and the two pentagons and 400 other yods. The former is denoted by the number 4 of daleth (ד) and the latter is denoted by the number 400 of tav (ת). The number of Daath is the number of yods needed to construct that part of the first (4+4) enfolded, Type A polygons that is not shared with the outer Tree of Life.
The number of Daath can be represented in terms of pentagramic arrays of the cubes of the Pythagorean integers 1, 2, 3 & 4:
The number of Daath is also the sum of the Godname numbers of the six Sephiroth of Construction above Malkuth:
the two overlapping triangles in the Star of David denoting the two triads of Sephiroth of Construction, viz. Chesed (31)–Geburah (36)–Tiphareth (76) and Netzach (129)–Hod (153)–Yesod (49). This identity may be interpreted as signifying that the six Sephiroth of Construction above Malkuth (the Sephirah whose Godname number is absent from the sum) determine the mathematics ("knowledge") of the Malkuth level of the Cosmic Tree of Life, i.e., the physics of the space-time continuum. They manifest as the six compactified dimensions of space predicted by superstring theory, the 10 dimensions of space-time corresponding (that is, being analogous) to the 10 Sephiroth, so that the three large-scale dimensions correspond to the Supernal Triad of Kether, Chokmah & Binah (see also here).
The gematria number of Daath is discussed further here (pp. 6-11).
