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## Internal Energy Boundaries | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Internal energy boundaries provide a precise, formal representation of an easily grasped idea. The question is: "how many times do the lines change from yin to yang, or yang to yin in the hexagram?" Why would this be of interest? It seems that one could interpret this as a measure of the "smoothness" of the energy in a situation: if the lines change back and forth from yin to yang and vice versa a lot, then there are a lot of energy transitions within the hexagram and the situation will be correspondingly "lumpy". Conversely, if there are very few transitions within the hexagram, then the internal structure of the situation will be "smooth".
The formal definition below tells you how to count the internal energy boundaries of a hexagram. If you don't speak Prolog, then skip on to the tabulation of the results, ## Logical DefinitionsIn terms of a recursive logic programming clause using Prolog-like syntax, the function to compute the number of internal energy boundaries would be: ieb([A|R]) = ieb(R, A, 0). ieb([], _, S) = S ieb([A|R], A, S) = ieb(R, A, S) ieb([B|R], _, S) = ieb(R, B, S+1) Then, if you feed a hexagram into this clause, it tells you how many internal energy boundaries the hexagram has: ieb() = 3 ## ResultsUsing this function it is quick to enumerate all of the hexagrams and sort them according to the number of internal energy boundaries they have. This gives the following table. The lattice picture on the right of the table links to a page describing the algebraic properties of the resulting sets of hexagrams.
## Some ObservationsThe following remarks summarize the observations detailed on the individual lattice-based pages. Firstly, the only hexagrams with no energy boundaries are the two pure hexagrams, Receptive and Creative. These define the axis for the first Chorand sphere, and the energy axis of all algebraic structures. These also form the only invarient cyclic wave sequences. Similarly and symmetrically, the hexagrams with the maximum number of energy boundaries and define the axis for the second Chorand sphere. These also form the only cyclic wave sequence of length 2. The hexagrams with one, or fewer, energy boundaries form a set containing exactly those hexagrams in the traditional seasonal cycle. This cycle forms a circumpolar loop around the first Chorand sphere. Further, the algebraic arrangement of those hexagrams matches the actual arrangement of the seasonal cycle. Then, the hexagrams with two, or fewer, energy boundaries form a set containing exactly those hexagrams which appear in Chorand's Receptive/Creative sphere. Also, they define the hexagrams which appear in coherent cyclic wave sequences. Those hexagrams with 3 or more energy boundaries make up the second Chorand Sphere. They are also the hexagrams which make up the dispersed cyclic wave sequences. The detailed meaning of these observations is explored in the subsequent sections. |

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