Wen Zhang

Web Notes

The following research notes, presented in HTML format, detail ongoing work, sometimes directly in response to a external ideas.  Where the material resented here assumes that you've read something from the PDF papers, this is made clear. However, at the least, you should probably have read Boolean Algebra and the Yijing before proceeding.

Subspaces and Unfoldings

The expanded seasonal cycle is special case of an unfolding. This takes the traditional sequence of twelve waxing and waning symbols and embeds them within an extended lattice context.

Exploring a Cubic Subspace - this note is a worked example of the cubic sublattice generated as the representation of the change from Binding Greatness to Spark from Fire. This is intended as a supplement to the paper Flowers and Steps in the Boolean Lattice of Hexagrams, and I recommended reading that paper first.

Unfolding Some Narratives - in my paper The Yijing as a Symbolic Language of Abstraction I suggest that the representation of perspectival unfoldings can be given a narrative. These web notes present the narratives for some selected unfoldings.

Waves and Spheres

The next items are all interconnected. The first three germinated as a result of some messages exchanged with Denis Mair and Henri Chorand on the Yixue mailing list. The notion of internal energy boundaries, formalized below, but common to a number of trains of thought, is connected to both wave sequences and Henri Chorand's spheres, and wave sequences are significant in both the Chorand spheres and the Teikemeier/Drasny sphere.

Internal Energy Boundaries - this provides a quantitative analyses of one way in which the energy within a hexagram changes by looking at the transitions between yin and yang across the lines of the figure.

Wave Sequences - in this section I look at how waves of yang can move through the background yin in coherent patterns.  The different types of wave that can arise are related to aspects of the internal energy boundaries discussed above.

Chorand's Spheres - this section describes an elegant and important construction developed by Henri Chorand which allows us to orient the six-dimensional Boolean lattice in three-dimensional space in a variety of interesting ways.

The Teikemeier/Drasny Sphere - this is another ingenious attempt to flatten the natural six-dimensional structure of the gua into a single three-dimensional structure. It's very interesting, and has some intruiging groupings. Further, it finds a natural place within the framework of the Boolean lattice and Chorand Spheres.