The Hexad is the first perfect number: it arises, by multiplication (rather than addition) from the Dyad and the Triad, and is hence termed “marriage” (whereas the Pentad is androgynous). That is, the Hexad unifies Male-Female through “blending” and harmony, rather than sticking them together through addition in the Pentad, in which case (because the Pentad is 2:3), one or the other prevails; with the Hexad, there is a perfect mixing.
There are six directions: back and forth, up and down, left and right; so Reality’s spatial structure reflects the Hexad. Furthermore, if one divides all number series into Triads, they reflect (in one way or another) the Hexad. 1+2+3=6, 4+5+6 = 15, and 1+5 = 6 again (not to mention that the Hexad is a second Triad), 7+8+9= 24 and 2+4=6, etc. (Readers who are familiar with traditional astrology will recognize the summing of the individual digits of sums to reduce the number to a simple one).
6 is the sum of it’s multiplicative factors, which are all prime (1x2x3=6).
Here are some of its titles: Resembling Justice The Thunder-Stone, Amphitrite (Poseidon’s wife; a verbal pun: on both sides [amphis] three [trias]), Male-Female Marriage, Finest of All In Two Measures, Form of Forms, Peace, Far-Shooting (name of Apollo) Thaleia Kosmos, Possessing Wholeness, Cure-All (panacea), Perfection, Three-Fold Health, Reconciling.
The Pythagorean theory of musical harmonies (which is really, as Iamblichus states, no “theory” at all, but rather “the way things actually are”) is fairly complex and is also related to Number.
The Pentad is the beginning of Life on the lower planes, but it is through the Hexad that actual re-integration occurs. In searching for other insights to this piece, I came across St. Nicholas of Flue, whose had a vision of “Two Trinities” : one was of the “old gods” of the West, and one was the newer, Christian perichoretic Trinity. Tomberg gives the key to interpreting some of this, when he notes that the two triangles of the key of Solomon symbolize the movement of lower Creation upward and the the movement of Spirit downward, integrated through the mediation of the regenerated man. Thus, we can see that the “old gods of the West” are not to be seen as “un-Christian”, but are rather, to be baptized and lifted up, through a process of cultural acclimation, in which Western Man is re-integrated into the prime Tradition through participation in Logos. This would (obviously) occur at both an individual and a corporate level, and beautifully illustrates how Christendom was designed to “give the pattern” or archetype to “men of the West”.
Nicholas of Flue, incidentally, is also credited with preserving peace between the Catholic and Protestant cantons of Switzerland through his sanctity, and of being the father of the “state” of Switzerland. The reader can see through this how Iamblichus’ “Numbers” are not mere arithmetic or private meditation only, but are indeed true understandings of how the entire Cosmos functions, at both lower levels and higher ones, physical or spiritual, and by implication, everything in between as well.