Boolean Algebra and the Yi Jing 4. Correctness and Correspondence

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Introduction

Much of the commentary for the individual lines in various versions of the Yi Jing are concerned with the issues of correctness, holding together and correspondence. For example, the work of Cheng Yi applies the theories of Inner Design to develop a detailed commentary of the Yi that reflects the application of these concepts. Cheng Yi's work is translated as The Tao of Organization by Cleary [Cle88] and I will have recourse to make extensive reference to this commentary throughout this paper. I shall begin, in Section 4.1 by describing the traditional notions of correctness and correspondence, as presented by Cleary and Cheng Yi in [Cle88]. This includes a description of the roles of the individual lines, as this helps to provide a context for understanding the significance of correctness and correspondence when used in interpreting the structures of the Yi.

Then, in Section 4.2, I shall present a method for representing correctness and correspondence, using the algebraic tools discussed earlier. I shall use those techniques to develop formal definitions for these properties and then use those definitions to prove some interesting characteristics. In particular I shall show that correctness and correspondence are interconnected properties, rather than two unconnected notions. As an interesting aside I shall also show how correspondence can be used to provide a method for classifying the hexagrams into eight classes. I shall not discuss the property of holding together in this essay.

Because of the extensive use of Cleary's translation in this paper I have decided to adopt the names of the hexagrams used there, rather than the more familiar translations offered by Wilhelm. To make things easier on the reader I therefore also include the King Wen sequence number and a linear binary representation of the gua where appropriate.

The remainder of this section is divided as follows:

• The Traditional Perspective
  • The Individual Lines
  • Correctness
  • Correspondence
• The Algebraic Perspective
  • Correctness
  • Correspondence
  • Correspondence Classes
  • Relating Correctness and Correspondence

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All material on this page copyright Dr Andreas Schöter

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