The Looking Glass Tree of Life

The Tree of Life is perhaps the most venerated symbol of the Holy Qabalah. In this diagram is distilled the essence of the Hebrew system of number mysticism. It consists of 10 sefirot, (or spheres), representing the Decad, among other things. Between these sefirot are 22 connecting paths, representing the 22 letters of the Hebrew Alef-bet, among other things. Altogether they comprise what is known as the “Thirty-two Paths of Wisdom.” This essay presumes basic knowledge of the Tree on the part of the reader.

This venerable diagram will be absorbed into the Trigrammaton Qabalah by means of a new formulation, called the Looking Glass Tree of Life. This name is derived from the structural nature of the Tree, when it is synthesized with the 64 I Ching hexagrams.

The general idea for this Tree comes from Fra. RIKB's suggestion that the 32 Paths of Wisdom could accommodate the 64 I Ching hexagrams, arranged in pairs. The Looking Glass Tree employs 32 pairs of antigrams for this purpose. That is, each hexagram is paired with its opposite on each of the paths. Within this overall scheme, there is a further division into types of paths, (sefirot, vertical, horizontal, diagonal), and types of lines, (Yang or Yin), as they appear in the hexagrams of the I Ching.

The 64 I Ching hexagrams come in 7 groups, based on the number of Yang lines within:

0 Yang lines = 1
6 Yang lines = 1
5 Yang lines = 6
4 Yang lines = 15
3 Yang lines = 20
2 Yang lines = 15
1 Yang lines = 6
Hexagrams = 64

Pairing these as antigrams, we have the following groups:

0 Yang & 6 Yang lines - 1 pair
5 Yang lines and 1 Yang line - 6 pairs

These 7 pairs make up all 7 of the vertical paths of the Tree.

4 Yang lines & 2 Yang lines - 15 pairs

These 15 pairs make up the 12 diagonal paths and the 3 horizontal paths.
The horizontal paths are the 3 pairs of this group that remain the same when reversed.

3 Yang & 3 Yang lines - 10 pairs

These 10 pairs are attributed to the 10 sefirot, having equal amounts of Yang and Yin.
The Middle Pillar sefirot contain hexagrams whose antigram and reversal are identical.

Thus, the types of hexagrams are closely correlated with the types of paths on the Tree.

The attribution of hexagrams to paths is anything but arbitrary. Having divided them into groups based on their Yang lines, and then pairing them as antigrams, it remains to determine which pairs are on which path. This has been accomplished by placing them in such a way that whenever possible, a path shares a pair of upper trigrams with one of the spheres it connects to, and shares its lower trigrams with the other sphere it connects to.

The exceptions to this occur on the vertical paths. Of these 7 paths, 6 of them have only one trigram pair in common with one of the sefirot they connect. Only the central path of the Middle Pillar follows the general rule, and shares upper and lower trigrams with the sefirot it connects to.

So, all paths of the Looking Glass Tree partake of the trigrams of the two sefirot they connect, except the verticals, which partake of only one of the sefirot. In these six cases, the remaining “non-shared” trigrams are always the Pure Yang and Pure Yin. This is a natural result of working within the constraints of this diagram. But it also says something about the nature of the pure Yang and Yin, for these descend directly out of the Crown of the Tree. They end up in Tiferet, where they split up and mingle with each other. It must be conjectured that at the same time, this “Descent of the Yang and the Yin” is occurring on the side pillars as well.

Several different variations of the Tree of Life structure exist, and all of them were explored in the creation of the Looking Glass Tree. It turned out that the Golden Dawn model of the Tree, derived from Athanasius Kircher, worked the best in terms of the sharing rule for trigrams. This rule makes it necessary for Tiferet to have more paths to it than the other sefirot, due to the function of the pure Yang and pure Yin trigrams, and their appearance within various hexagrams.

A brief explanation of the Middle Pillar is in order here. Coming from Malkut, one starts with the four “unbalanced” I Ching trigrams, (these same four are found in Keter as well). From there the adept encounters the group of 4 balanced trigrams found on the path to Yesod. This allows the sphere of Yesod to be reached via the Middle Pillar. Once there, one encounters the last 2 hexagrams of I Ching, with mingled Fire and Water trigrams.

So, in a sense, if we all start in Malkut, and the four trigrams there are just “given” as part of the fabric of experience, then it is not unreasonable to suspect that the remaining four trigrams will be “given”, (if not earned), on the path of ascent, thus arming the adept with all the necessary tools to travel the remainder of the Tree.

The next path upward, between Yesod and Tiferet, shares trigrams according to the normal rule. Then we encounter another path that doesn't share trigrams. This is the path across the Abyss, which requires the pure balance of the Creative and Receptive to accomplish. This is, in effect, a rearranging of everything that happens in Tiferet. From there, one arrives at Keter, (also called Ratzon), and reverts back to the four “unbalanced” trigrams that they started with, only reversing their upper and lower positions.

So the hexagrams are arrayed on this Tree in a very particular order. But there is one more subdivision to be made. The Looking Glass Tree is actually two Trees, a Daylight Tree and a Nightside Tree. The Daylight side is the “normal” Tree, and the Nightside is the Qelipot, the shadowy half of the Tree. Since the term Yang means light, and Yin means shadow, we may refer to them as the Yang and Yin sides of the Tree. These two sides are mirror images of each other, giving the Looking Glass Tree its name.

Antigrams are on opposite Trees, but so are Reversals.

The two different Trees are symbolized by the coloring used in the diagram. The red hexagrams are on the Yang side of the Tree, the blue are on the Yin side. If you reverse any red hexagram, it becomes blue. This shows that we can access the shadow of any path by either considering the antigram, or the reversal.

These two Trees are literally mirror images of one another. Using the diagram where the I Ching hexagrams have been rotated anticlockwise, print this out, hold it up to a mirror, and see that the exact same Tree results, but flipped on its vertical axis. In other words, the pair that was in Chesed is now in Geburah, only the colors have changed. And those hexagrams on the Middle Pillar will become each other when reversed, (same pair, new colors), while the horizontals will remain the same, since they are reversible by definition.

Reversals appear on opposite sides of the Tree, except for the horizontals and the spheres of the Middle Pillar, (which are pairs of reversals to begin with). The last strange thing, the one “leak” in this symmetry, is that by reversing the hexagrams of the path from Malkut to Yesod, you get the hexagrams for the path from Yesod to Tiferet; these are the only two paths which “switch places” when the hexagrams of that path are reversed. Everything else is in a beautiful state of symmetry.

The Looking Glass Tree of Life – Numerical Data

Each of the 32 “Paths of Wisdom” contains a pair of I Ching antigrams. All such antigram pairs sum to the same number: 1092. This is a “group number” for antigrams, which always sum to one of 63 possible numbers, (93, 111, 813, etc.). The value of any of these group-numbers is based on the root-pair of the group. The root-pair always has only Yang (and/or Tao) lines in one hexagram, and only Yin (and/or Tao) lines in its opposite. So the root-pair for the I Ching antigrams is 364 and 728, because in Base-3 these are 111111 and 222222. This is the basic pair that defines the group.

1092 = if only the Zelator blow sufficiently upon his furnace, all the systems of earth are consumed in the One Knowledge. (Liber Porta Lucis sub figura X, verse 20)

The L.G. Tree is divided into a Yang side and a Yin side, based on the antigrams. The sum of the hexagrams on each side of the Tree is as follows:

The Yang side Tree hexagrams of all 32 paths: = 17,290. (incl. 5460 for the Sefirot)
The Yin side Tree hexagrams of all 32 paths: = 17,654. (incl. 5460 for the Sefirot)

This is a discrepancy of exactly 364. In this arrangement, there is an excess of forces on the Yin side of the Tree. However, if one simply ignores the pair of hexagrams 364 & 728, which are on the path across the Abyss, there is a perfectly symmetrical result:

Yang side Tree hexagrams total: 17,290 - 364 = 16,926
Yin side Tree hexagrams total: 17,654 - 728 = 16,926

In effect we are counting the numerical value of the hexagrams of only 31 of the paths. The path across the abyss is not included, thus keeping everything in balance. By removing this basic pair from consideration, leaving 31 pairs of hexagrams on 31 paths as the subject of the calculation, we arrive at the following:

Yang side Tree hexagrams total: 17,290 - 364 = 16,926 = 182 x 93
Yin side Tree hexagrams total: 17,654 - 728 = 16,926 = 182 x 93
So the total of all the hexagrams in our set is now: 33,852 = 364 x 93.

This factor of 93 represents the word Thelema. It is yet another characteristic of this Looking-Glass Tree which shows it to be purely Thelemic in nature.

364 = the great mystery of the House of God = God is One; God is the Everlasting One;

The Tree is split in halves; each side has hexagrams that equal 93 x 182:

182 = the First and the Last = by two and by two

The root-pair of the I Ching hexagrams is 364 & 728. They differ by 364. If we remove this pair from the total value of the Tree, we must then remove their difference-value as well. This leaves us with the sum of 31 unique numbers. The sum of the difference-values of the 32 antigram pairs is 6196 - 364 = 5832 = 729 x 8

The operation of 729 times 8 recalls the phrase found in Liber A’ash vel Capricorni:
I am Baphomet, that is the Eightfold Word that shall be equilibrated with the Three

Crowley discovered the true spelling of this name. To him, Baphomet was spelled in Hebrew as , BAVOMIThR, so that it would have 8 letters that total 729. This fulfilled the conditions of the verse, because the 8 letters made the name “eightfold”, and the value of 729 made it “equilibrated with the Three” because 729 is 3 to the 6^th power. So taking this very important number, 729, and making it literally “eightfold” by multiplying it with 8, gives us the total difference-values of antigram-pairs of the Tree.

In both cases, (the sum of the hexagrams, and the sum of their difference-values), by ignoring the root-pair we get very significant qabalistic numbers. This obviously lends a great symbolic weight to the pair that is removed. They are the axis upon which the other hexagrams spin. Their special status is symbolized by coloring them green.

These 2 hexagrams descended directly from the first sphere of , Ratzon or “Will”, right into the heart of the Tree, thus informing all the vertical paths, (those which don't follow the sharing rule completely). The fact that we make this primal pair “disappear” ino urcalculations, explains why the pure Yang and pure Yin trigrams appear on the Tree, as we drop down from the Supernal Triad. They are, in fact, our Pure Will descended into consciousness. They are the observation deck of the Tree of Life.

As if to reinforce this idea, the first sefira holds the pair of hexagrams 395 & 697. These are the only antigram pair whose values differ by the number 302:

302 = Do what thou wilt shall be the whole of the Law.

The difference-values of the antigrams on the 10 Sefirot, and their gematria equivalents:

In studying the Tree, the two most important subsets are the three Triads and the Middle Pillar. The Triads are simply the spheres taken in groups of three: spheres 1, 2, & 3; spheres 4, 5, & 6; spheres 7, 8, & 9. The Middle Pillar spheres are numbered 1, 6, 9, & 10.

The sum of the differences of the Supernal Triad is 302 + 286 + 130 = 718.
The sum of the differences of the Middle Triad is 142 + 178 + 338 = 658.
The sum of the differences of the Lower Triad is 194 + 290 + 182 = 666.

718 = And the Magus is Love, and bindeth together That and This in His Conjuration.
658 = Khabs is the name of my House. In the sphere I am everywhere, the centre,
666 = the Magus is Love, and bindeth together That and This in His Conjuration.

The sum of the difference-values of the Middle Pillar is 302 + 338 + 182 + 146 = 968.
This is highly significant, as Hadit describes the Kundalini serpent found in the spine:

968 = If I droop down mine head, and shoot forth venom, then is rapture of the earth, and I and the earth are one. (Liber CCXX 2:20)

968 also provides a description of the nature of the Magus in the following quote:

968 = How then shall He end His speech with Silence? For He is Speech. He is the First and the Last. How shall He cease to number Himself? (Liber B vel Magi vv. 3-4)

The difference-value of the final sphere, Malkut, is 146. Therefore the sum of the difference-values of all 10 spheres is 718 + 658 + 666 + 146 = 2188.

Note well this number 2188, for in Base 3 notation it is: 10000001.

This number is highly symbolic: it represents the smallest number in which the Zero hexagram is “concealed”.

2187 = 3^7. This number is the first Octagram. By adding 1, or Yang, to it, it becomes 2188, and the Zero hexagram is concealed within it. It is therefore like an egg. One might even say that 2188 is the number 10 writ very large, for in Base 3, the decimal number 10 is written as 101, and is the first number to “conceal” the Tao within itself.

As the verse for the 10 trigram in Liber Trigrammaton says: “Also certain secret ones concealed the Light of Purity in themselves, protecting it from the Persecutions.”

Note that the word Concealed = 93, and is quite involved in the unraveling of the gematria of Liber CCXX. Note also that one of the titles of the first sphere in the Hebrew Qabalah is “the Concealed of the Concealed.”

Concealed = 93 = = WILL = 10 (by TEG)

The Ten trigram reveals the importance of the concealment, and when it is written very large, as 10000001, it shows the difference-values of the 10 spheres of the Tree. These 10 spheres represent WILL in all its forms. The whole Tree is Will, deriving from , Ratzon, just as surely as 10 derives from 1, and is a higher octave of 1.

Thinking then about the Hebrew qabalistic symbolism of this 10, we must also include the letter Yod, y, the Hadit-point, the Hermit, the smallest letter, of which all other letters are extensions. This letter has a value of 10. 

In Liber ARARITA, the chapter headed by the Hebrew letter begins by describing this Hadit-point. The gematria suits our symbolism perfectly:

2188 = the indivisible point which hath no points nor parts nor magnitude. Nor indeed hath it position, being beyond space. Nor hath it existence in time, for it is beyond Time. Nor hath it cause or effect, seeing that its Universe is infinite every way

2188 is the grand total of the difference-values of the antigrams on the 10 spheres. But of equal importance are the numbers that generate these differences in the first place.

The charts below contain the Base-3 values for the antigram pairs of the 10 spheres, as well as their TQ gematria equivalents, taken from The Holy Books of Thelema.