The above diagram shows two aspects of 'The Word' - my interpretation of the Kabbalist root. On the left, the see the four-way complementarity of the Four Principles of Organisation. In other words, all identifiable units require the four principles for their complete description. On the right we see the hierarchical nature of the principles - the 'First Principle' describing the complete individual and also its component parts at a different hierarchical level.
If we combine this with the topology of Human living then each of the three visible levels requires a fourfold description for their inner workings. For the Tropical Zodiac, we see
Level 1 as the set {Aries, Taurus, Gemini, Cancer},
Level 2 as {Leo, Virgo, Libra, Scorpio} and
Level 3 {Sagittarius, Capricorn, Aquarius , Pisces}. These Signs are related to the attribute set {Fire, Earth, Air, Water} - one instance of the Four Principles. This is the simplest way to explain why there are exactly twelve Signs of the Zodiac. Here we have the 'proof of the pudding', confirming that the modelling is correct.
Just a reminder of the spatial topology where the cut-out region (2) of the sphere (left) is topologically equivalent to a plane - astrologically, the Plane of the Horizon.
And finally, the base-4 arithmetic of Astrology, where each element has a two-digit value {Level, Active Principle}. Each is the root value for a family of components. For example {3, 4} includes Pisces, the Twelfth House and the planetary principle, Neptune.
Hopefully, the updated model of Astrology begins to become more clear. All the mathematics used in my work is explained in Appendix A of the book.
Henry.