The Kabbalah – the tetractys seen differently
Ten sephirot in four worlds, ten "numbers without anything" in the Book of Creation, and 231 gates from 22 letters that form a 22-gon simplex.
Anyone who knows the basics of the Kabbalah knows the tree of life with its ten sephirot in four worlds. In numbers: ten sephirot spread over four worlds, like the tetractys, 1 + 2 + 3 + 4 = 10. The tree shows how ten principles emanate from one divine cause, pour forth and take shape.
The tree of life with the ten sephirot. The colours assign them to the four worlds, as the tetractys can be read in it: 1 in Atziluth, 2 in Beriah, 3 in Yetzirah, 4 in Assiah.
The Kabbalah asks how the human being is bound to God. Three foundational writings belong to it: the Sefer Yetzirah, the “Book of Creation”, the oldest, the Zohar, the “Book of Splendour”, and the teaching of the Merkabah, the divine throne-chariot from the vision of Ezekiel. Many later books on the mysticism of letters and numbers, on magic or Christian Kabbalah contradict each other on important points and should be read with caution. Anyone looking for firm ground in this thicket finds it in number and figure, because they can be checked.
Two sides of one coin
The Sefer Yetzirah and the Pythagorean tetractys are two sides of the same coin: both claim to describe the nature of creation. As early as 1494 Johannes Reuchlin, in De verbo mirifico (On the wonder-working word), compared the four-letter name of God YHWH with the tetractys. In some depictions, for example by Papus, the Tetragrammaton is indeed arranged in a triangle, exactly like the triangle of ten points: Y, YH, YHW, YHWH, ten letters in all.
Ten numbers without anything
The Sefer Yetzirah describes creation through “thirty-two hidden paths of wisdom”: ten numbers “without anything” (the sephirot) and the 22 letters of the Hebrew alphabet, divided into three mothers, seven doubles and twelve simples. The text stresses the ten emphatically: ten and not nine, ten and not eleven. It compares them with the ten fingers, five opposite five. Their measure is ten, yet they are without limit. Their end is bound to their beginning like the flame to the coal. And it calls on the reader: know, count and draw.
This is no mere coincidence. The geometry of the circle as the idea of creation, from the spiritual into the material, has a long tradition in the secret teachings. Simplexes and fractal polygons, crystal lattices and sphere packings: this is the geometry of perfect symmetry, of circle and sphere. In their original form, so the thesis goes, these connections also stood godparent to the Kabbalah. The spatial lattice of the densest sphere packing probably also lies behind the creation account of the Sefer Yetzirah (see Gap-free filling of space): there first a tetrahedron, then an octahedron and finally a cube become visible.
The golem and the 231 gates
Besides the tree of life there is a second Kabbalistic practice linked to the idea of creation: the making of a golem, a servant being of clay. The traditions describe a strictly regulated ritual: the adept works with at least two companions, purifies himself in body and mind, wears white garments and works at night, when the darkness recalls the time before creation. The golem is formed from untouched earth and fresh spring water. For bringing it to life there are highly contradictory instructions, with names of God of four, twelve, 24, 48 or 72 letters. The best-known golem legend is that of Rabbi Loew in Prague.
To bring the individual limbs to life the adepts drew on the Sefer Yetzirah. It says the 22 letters were engraved, hewn, weighed, permuted and combined. Because Hebrew writes no vowels, the verse can also be read as a command: engrave them, hew them, permute them! The Sefer Yetzirah calls chaos the primal substance of creation. Into this chaos it places 231 gates, “in a circle like a wall”: all possible pairings of two of the 22 letters, without repetition.
The ritual consisted in visualising each letter (engraving), separating it from other thoughts (hewing) and joining it with all the others (permuting): first aleph with every letter, then bet with every letter, and so on round the whole circle, sung, quickly and without pause. Each letter belongs to a part of the body, and limb by limb the golem was meant to come into being.
The diagram for this practice is nothing other than a 22-gon simplex:
The 22-gon simplex: 22 points, each joined to every other. That makes 231 lines, the 231 gates of the Sefer Yetzirah, and 231 is the triangular number T(21).
A tongue-in-cheek interpretation: the dutiful adept will intone, engrave and permute until he pauses and reflects. If he is awake in mind, he recognises that the combinatorics of this practice contain a deep truth. He need only take seriously what the Sefer Yetzirah says: know, count and draw! Then he arrives at the insights that matter here: number theory + geometry = philosophy.
A traditional Kabbalistic amulet combines pentagram, hexagram and octagram, figures that play a special part in this geometry.