Charged Sets of the Trinity

The Triform Energy Cascade (TEC), is a theoretical structure first postulated by Fr. RIKB, which uses a trinity to create 26 sets that align with the major categories of an English Qabalah.

Suppose that there are 3 entities, which we might call ‘charges’. These charges are represented by a positive, negative, and neutral, or +, -, and 0. Such a trinity may be symbolized in a multitude of ways, such as Sulfur, Salt, and Mercury, or Thesis, Antithesis, and Synthesis. In order to align these charges with the ternary system of Trigrammaton, they are symbolized with the numerals 1, 2, and 0.

The idea behind the TEC is the grouping of these charges in sets of 1, 2, 3, or 4 members. These groupings are done without regard to permutation, such that the set with members {1, 2, 0} is the same thing as the set {0, 2, 1}. There are 35 such sets, including the Empty Set:

The method that creates 26 specific sets among these 35 is the idea of a “charged” set. The 0 is considered as neutral, and the 1 and 2 are positive and negative charges that cancel out to zero. Therefore, any set that is composed of 0s, or equal numbers of 1s and 2s, or any combination thereof, is considered a “neutral set”. These 9 sets are maroon colored in the chart above. The remaining 26 sets, colored chartreuse, are considered “charged sets”, since they have an excess of either a positive or a negative charge.

Of the charged sets, there are 2 that have one member, 4 that have two members, 8 that have three members, and 12 that have 4 members. Not only does this not follow a simple doubling scheme, (which would result in 16 sets having four members), but the number of sets aligns exactly with the categories of the Western occult tradition.

The 2 charged sets having one member each represent Yang and Yin, or the pure Positive and Negative charges. The 4 charged sets having two members represent the four elements of Fire, Water, Air and Earth. The 8 charged sets having three members represent the seven classic Planets, plus Earth. The 12 charged sets having four members each represent the 12 Zodiac signs of astrology.

The first thing to note about the sets of the TEC is that the number of sets in each column is a “triangular” number. A triangular number is a term invented by the ancient Greeks that refers to the number of dots that can be arranged into an equilateral triangle. Thus the first five triangular numbers are 1, 3, 6, 10, and 15. We can arrange these 35 sets into an array of increasingly larger triangles, beginning with the Empty Set.

By considering the circles as vertexes, and stacking these five triangles on top of each other, we can create a “four-frequency” tetrahedron (4F tetra). This name is derived from the four vectors along each edge. Below is a model of such a tetrahedron.

The 4F tetra is the smallest tetrahedron that has a “nuclear” vertex. If these vertexes were spheres, there would be one sphere at the very center, surrounded by twelve other spheres. This nucleus represents the neutral set of {0, 1, 2} in the TEC.