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The Culver Lattice

Introduction

Billy Culver's lattice is one of the most interesting and innovative structures that I have seen applied to the Yijing. He provides no technical discussion himself, instead relying on a series of diagrams to develop his ideas. His Energy Language site can currently be found on Google sites. The main structure that I will be discussing here is his 6 bit semiprocess diagram, which used to know as a Fluvial Polar Diffusion Lattice.

In the following pages I will introduce formal rules that encode the Culver lattice structure. The development of these rules will allow a direct comparison with the Boolean lattice. Note that my individual gua pages in my Hexagram Navigator already contain details of both the Boolean and Culver lattice structures for each symbol (see, for example, the page for 111000).

There are also diagrams of the complete Boolean lattice and complete Culver lattice. You should probably start with a good look at these two diagrams so you can see exactly what is being compared in the following pages.

Note that the formal rules are written in Prolog. If you don't know Prolog, you can skip the technical definitions and still get a good sense of the discussion by studying the diagrams.

The Covering Relation

CoveringThe most direct characterization of the structure is through its covering relation. This describes how one gua connects to another.

There are further sections to come in this study, including: a discussion of the ordering relations that are derived from the covering relations; a discussion of magnitude and the resulting layers in the lattice structures; and a comparison of the two structures.


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