Mathematical representation of the hermetic axiom "As above, so below"
The ancient Greeks gave the name of Hermes Trismegistus ("thrice-great Hermes") to the Egyptian god Thoth, or Tehuti, a god of learning and wisdom, who was the scribe to the other gods. According to legend, Hermes Trismegistus provided the wisdom in the ancient mysteries of ancient Egypt: "He carried an emerald, upon which was recorded all of philosophy, and the caduceus, the symbol of mystical illumination. Hermes Trismegistus vanquished Typhon, the dragon of ignorance, and mental, moral and physical perversion."  Called "The Emerald Tablet,"* its most significant part is within its opening: "That which is above is like that which is below and that which is below is like that which is above, to achieve the wonders of the one thing." Therefore, "This is the foundation of astrology and alchemy: that the microcosm of mankind and the earth is a reflection of the macrocosm of God and the heavens." This metaphysical statement has been abbreviated to the saying "As above, so below." As 'Earth' (meaning, of course, the physical universe, not just the planet Earth) is Malkuth, symbolized by the hexagonal yod at the centre of a tetractys, this hermetic principle is mathematically implemented in terms of the Pythagorean tetractys by replacing the 1st-order tetractys symbolizing Malkuth (the "below") at the centre of the 2nd-order tetractys by a 2nd-order tetractys that represents the "above". Instead of 49 hexagonal yods symbolizing Sephiroth of Construction (42 in the six tetractyses symbolizing the six Sephiroth of Construction above Malkuth), there are in the modified 2nd-order tetractys (49+42=91) hexagonal yods with seven prismatic colours that symbolize the seven Sephiroth of Construction. Alternatively, circular yods can be replaced by triangles, white triangles referring to Sephiroth that belong to the Supernal Triad and coloured ones referring to Sephiroth of Construction. Either representation is what can be called the "Cosmic Tetractys" that maps the physical and superphysical cosmos. Par excellence, it expresses this famous hermetic principle. The 49 coloured triangles in the central 2nd-order tetractys express the 49 differentiations of the seven Sephiroth of Construction that refer to the Malkuth level of the Cosmic Tetractys. The 42 coloured triangles in the six tetractyses surrounding it express the seven-fold differentiation of the six Sephiroth of Construction above Malkuth. The Cosmic Tetractys is the Pythagorean way of representing the 91 differentiations of the seven Sephiroth of Construction, as  symbolized by the seven hexagonal yods in the tetractys. It is a geometrical way of embodying the hermetic principle that the macrocosm is the same as the microcosm — both physical and superphysical. Or, more accurately, they are analogous. The Emerald Tablet expresses a powerful, alchemical formula that, once followed, can accelerate one's spiritual evolution to enable conscious entry into the Life of God, thereby ending the cycle of birth, death & rebirth. The Cosmic Tetractys maps the stages in that journey. It is a kind of Pythagorean mandala. The sacred geometries of other religions, too, are maps of all levels of reality. The great miracle is that they are equivalent, i.e., they map the same Cosmic Reality in analogous ways, as this website (and, in particular, this section) proves. This conclusion has profound implications, for it is tantamount to being evidence for the existence of a transcendental Mind, the mathematical pattern of Whose thoughts is found to be the same when represented by certain sacred geometries (see The holistic pattern and Wonders of correspondences).

* Twelve translations of the Emerald Tablet of Hermes can be found here.

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