Lattice Structure Overview

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This page gives a description of the lattice structure pages for the gua, and how they are intended to be used. Because the lattice structures are quite large, especially for lattices of gua with a reasonable number of lines, each page only shows the immediate lattice locale for the primary gua under consideration.

Each page is composed of two main elements:

  1. The name of the primary gua.
  2. The lattice locale for that gua.

The Name

Each page has the name of the primary gua and a simple term showing its place in the lattice. For example, for the trigram Danger, the heading would be:
Danger (e1f2)
What this shows, firstly, is that the page shows the lattice locale for the gua Danger.

The associated equation e1f2 tells use where in the lattice the gua appears. These terms are elements from the standard lattice equations used by Sung [Sun69] and Higgins [Hig98]. Sung uses the arbitrary letters A and B (see his Trigram Space Equation), and Higgins uses the letters a for "active" (yang) and i for "inactive" (yin). In these pages I prefer to use the letters e for "energy" or yang and f for "field" meaning yin. Note that the term "field" for yin is taken from the translation of Ritsema and Karcher [R&K94].

In this case then, the term simply says, that the gua has one yang line and two line lines.

The Lattice Locale

The body of each lattice pages shows the primary gua under consideration near the centre. This gua is indicated by having a gray background. Clicking on the primary gua will take you to the main page for that gua.

Above and below the primary gua are those gua that are above and below the primary gua in the lattice structure. These are shown as connected with the primary gua by lines. Clicking on one of these connected gua will take you to the lattice page for that gua.

For a brief overview of lattice structures in the gua, please refer to the section on The Induced Ordering in the thread on Boolean Algebra and the Yijing.

In effect, each lattice page shows the gua "flower" for the primary symbol, with the connected gua in the lattice being its "petals". For a description of this idea see [Hac93, p94].

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