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#13 Correspondence between the 10-tree and the 64 hexagrams
Replacing each of the ten Sephiroth in the Tree of Life by another Tree of Life generates ten overlapping Trees of Life with 64 'Sephirothic levels' (SLs). 64 is the number value of Nogah, the Mundane Chakra of the Sephirah Hod, signifying mental activity and communication (see Table 1). 21 SLs (denoted by black dots) line the left-hand Pillar of Judgement, 21 SLs (denoted by white dots) line the right-hand Pillar of Mercy and 22 SLs (denoted by blue dots) line the central Pillar of Equilibrium. 21 is the number value of EHYEH (אהיה), the Godname of Kether.
Compare this with the 8×8 array of hexagrams that form the basis of the ancient Chinese I Ching
system of divination. It consists of 64 hexagrams. 22 blue ones line two adjacent sides and a
diagonal, 21 black hexagrams form a right-angled triangle on one side of the diagonal and
21 white hexagrams form a right-angled triangle on its opposite side. The hexagram (Chien) in
the top left-hand corner of the table is a pair of "Heaven" trigrams: 
. This hexagram corresponds to the first SL, namely,
Kether of the tenth Tree of Life. The hexagram (K'un) in the bottom right-hand corner is a pair of "Earth"
trigrams: 
. It corresponds to the last SL, namely, Malkuth of the
first Tree of Life, whose Mundane Chakra is the planet Earth. The 15 blue
hexagrams on adjacent sides of the I Ching table correspond to the uppermost 15 SLs on
the Pillar of Equilibrium. The remaining seven blue hexagrams on the diagonal correspond to the lowest seven
SLs on this pillar that belong to the two lowest Trees. This 15:7 division of hexagrams
reflects a 8:2 division of 10 overlapping Trees.
We can take the correspondence between ten Trees of Life and the 64 hexagrams deeper by replacing each of the 64 SLs of the former by complete Trees of Life. The number of SLs in 64 overlapping Trees of Life is 388. Below Kether, Chokmah & Binah of the highest Tree are 385 SLs, where
385 = 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102.
They comprise 384 SLs above Malkuth of the lowest Tree that are corners of blue or red triangles. Every successive Tree emanates six SLs made up of two triads (coloured blue and red in the diagram shown below) of Sephiroth of Construction: Chesed-Geburah-Tiphareth and Netzach-Hod-Yesod.
The 64 hexagrams correspond to the 64 pairs of triads of SLs in 64 Trees of Life, which express the 64 SLs in 10 Trees of Life representing the 10 Sephiroth of the Tree of Life.
The SLs (Chesed & Netzach) on the "male" Pillar of Mercy emanate SLs (Geburah & Hod) on the "female" Pillar of Judgement and their union are the SLs on the androgyne Pillar of Equilibrium (Tiphareth & Yesod). This swing between "positive", "negative" and "neutral" corresponds in Taoism to the interplay between the polar opposite phases called 'Yang' and 'Yin' and their balance in stable equilibrium. The 384 SLs form 64 pairs of triads (blue & red). They correspond to the 64 hexagrams, each one a pair of trigrams. The 64 blue trigrams are the counterparts of the 64 blue triads and the 64 red trigrams are the counterparts of the 64 red triads.
Superstrings
In terms of superstring theory, the 10 Trees represent dimensions of the 10-dimensional space-time that this theory
predicts, the lowest Tree denoting the dimension of time. Therefore, the two lowest Trees of Life denote time and a
large-scale dimension of space — the so-called "longitudinal" dimension, along which distance along the length of
the superstring is measured. The eight highest Trees of Life represent the eight so-called "transverse" dimensions
— the dimensions of space perpendicular to the superstring at any point along its length. So the
15:7 division referred to above reflects the primary division of superstring space-time into the
eight transverse dimensions, the longitudinal dimension and time. The same pattern manifests in the 10 superstring
dimensions and the I Ching table of hexagrams because the former constitute a holistic system represented by the
latter and —par excellence — the tetractys (see here). YAH (יה), the (older) Godname of Chokmah,
prescribes this division because its number value is 15.
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