Boolean Algebra and the Yi Jing

7. Notes
[1] Kirk McElhearn [McE98, p3], is the first person to use the term situation to refer to the underlying meaning of a hexagram in print. This is a fortunate use of terminology.

[2] The syntax used for these operators is the standard one employed in such programming languages as C and Java, rather than any of the equivalent notations used in mathematical logic. The author has developed an experimental set of programs written in the programming languages Java and Prolog that implement the operations discussed in this essay.

[3] I should note that the bulk of the work on this paper was done long before Goldenberg's work was brought to my attention by Steve Moore.

[4] A good introduction to the mathematics of such structures can be found in [D&P90]

[5] There is an interesting connection between the lattice structure and the polynomial space that Higgins investigates for the trigrams [Hig98]. Without going into details, Higgins places the trigrams in the space represented by (a+i)3 which expands to:

a3 + 3a2i + 3ai2 + i3

If we compare this with the lattice in Figure 2 we see that each term in the expanded polynomial relates to a distinct layer in the lattice. This connection needs to be investigated further.

[6] Wilhelm shows how this process can be extended all the way to the generation of the hexagrams [Wil82, Figure 1].

[7] I am grateful to Frank Coolen from the Hexagram 8 discussion list for clarifying the precise geometric nature of Cleary's Primal Correlate relation; this relation originates in Cleary's book I Ching Mandalas (see [Cle89]), to which I did not have access when originally writting this paper.

[8] A more detailed description of the property of Correctness is given by Wilhelm in Section 5 of "The Structure of the Hexagrams" [Wil83, pp360-361].

[9] Wilhelm discusses this relationship in detail in Section 6 of "The Structure of the Hexagrams" [Wil83, pp361-362].

[10] In fact, this is the relationship of holding together. Two lines may hold together when they are adjacent in a hexagram. This relationship does not concern me in this paper, but the interested reader is referred again to Wilhelm's "The Structure of the Hexagrams" [Wil83, pp362-364].

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