Chorand Spheres | ![]() |
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General Chorand SpheresIt is possible to generalize the notion of Chorand Spheres using Boolean algebra to define a construction which can be applied to any hexagram. At first, this might seem an unnecessary exercise. Afterall, the first Chorand Sphere is oriented on Receptive/Creative, the most pure hexagrams, and the second on the two poles of resonance The north/south pole of the earth is typically defined with respect to the axis of the planet's spin; this is so-called "true north". But there is also "magnetic north". Magnetic north deviates a few degrees from true north, but it nonetheless provides a useful frame of reference. In generalizing the Chorand construction, we acknowledge that Let us call the set of hexagrams defined by ieb < 3 the "Chorand Set" (or CS for short). Remember, this is set of hexagrams that appear in the Receptive/Creative sphere. We can now define a function as follows: chorand(H) = {G x H : G ∈ CS} This says that the Chorand function of a hexagram H is the set of hexagrams composed of G x H for each G in the Chorand Set CS. If we take G as Receptive, then we get the original Chorand Sphere as previously defined. If we take G as As an example, consider taking the hexagram As noted above, by taking hyperchorand(H) = chorand(H x This says that for any Chorand Sphere defined on hexagram H, the corresponding hypersphere composed from all the hexagrams not in the first sphere is simply the Chorand Sphere defined on H x Another general result of interest is chorand(H) = chorand(~H) This says that the Chorand Sphere defined on a hexagram H is the same as the Chorand Sphere defined on its Boolean opposite ~H. Exploring the extent of algebraic theorems that can be derived from these definitions remains an open topic. | ![]() |