## Mathematical Material |
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The material linked to on this page is of a fairly technical nature and generally assumes some background knowledge of the Yijing. Some of it is quite mathematical. However, the necessary concepts are fully explained. The papers are divided into two broad groups:
- Basic Framework - provides the necessary technical background.
- Traditional Applications - shows how the fomal techniques can be used to analyse traditional ideas.
- Contemporary Explorations - shows how the algebra gives rise to new forms of analysis.
- Diagrams - some structural diagrams of the symbols of the Yi.
Ideally, you should probably start with the paper describing the basic formal framework before moving on to read the applications papers. ## Basic FrameworkThis paper describes the formal logical background to much of the rest of my work. Boolean Algebra and the Yijing - this provides the necessary background to understand the mathematical techniques used in analysing the structures of the Yi. It takes a formal look at Cleary's ## Traditional ApplicationsThe papers in this section use the formal techniques discussed above to analyse some of the traditional and contemporary structural notions found in the Yijing. Correctness and Correspondence - this is a follow-on paper to "Boolean Algebra and the Yijing". It applies the mathematical tools introduced in the first paper to provide an analysis of the two traditional ideas of correctness and correspondence. This paper originally appeared in ## Contemporary ExplorationsFlowers and Steps in the Boolean Lattice of Hexagrams - this provides a detailed analysis of Karcher's The Yijing as a Symbolic Language for Abstraction - this paper, which originally appeared in a shorter form in the - The short version of the pape as published in the conference proceedings
- The extended abstract for the paper
- The powerpoint presentation of the material
- Detailed examples of unfoldings
The Yijing as a Mathematical Metaphysics - this is the full version of the paper which originally appeared in a much shorter form under the title "The Yijing: Metaphysics and Physics" the - The short version of the paper as published in the conference proceedings
- The extended abstract for the paper
- The powerpoint presentation of the material
- The script for the presentation
- A mathematical supplement
Bipolar Change - following from a conversation with Alain Stalder, this article extends the basic algebraic analysis of change, clarifying the relation between change as a yang energy and change as a yin energy. Extensive examples show how the technique can be applied to represent change through the lattice structure, change in correctness and change of resonance. A parallel is also drawn with the quantum theoretical phenomenon of vacuum polarization. A slightly shorter version of this article appeared in the Tools for Change - this is jointly authored with Stephen Karcher, and applies the mathematical tools introduced in the Boolean Algebra paper to some of Karcher's techniques of interpretation, showing how this can result in a rich set of images for a divination. It includes a formal analysis of the nuclear hexagram construction and Karcher's ## DiagramsMost of the following diagrams are high-resolution images, suitable for full page printing. Note that these diagrams open in a new window. It will probaly help to make sense of the unfoldings in particular if you have read the "Yijing as a Symbolic Langauge for Abstraction" paper above. The Whole Lattice - this diagrams shows the complete six dimensional lattice structure generated by the Boolean algebra. Explicate Matter Cubic Unfolding - this diagram shows how the lattice can be unfolded into a chain of three dimensional subspaces, based on the alternations of the lower trigram. Heart and Mind Planar Unfolding - this diagram shows how the lattice can be unfolded into a chain of two dimensional subspaces, based on the alternations of the middle bigram. If you want a set of images for displaying all the different individual gua, you may download and use the set that I created for this web site. They are zipped into a single file here. |