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The Yijing as a Symbolic Language for Abstraction Image and Number meets Boolean Algebra Dr Andreas Schöter Edinburgh, UK http://www.yijing.co.uk

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Overview The role of structure Dimensional progression Lattice of energy Represents the structure of reality Unfolding the structure Theory of individual perspectives

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http://www.yijing.co.uk Structure and Process Gua are energetically related to each other through lattice structures. The lattices relate gua along lines of energy difference. The lattice structures have meaning. The processes which generate the lattices have meaning.

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http://www.yijing.co.uk One Dimension Yin and Yang polarized in the basic lattice. Geometrically: a line, one dimensional. Energy order: –Yang, with most energy at the top. –Yin, at the bottom.

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http://www.yijing.co.uk One Dimension Link pairs of gua through a single changing line. One-dimensional structures are edges in the complete lattice.

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http://www.yijing.co.uk Two Dimensions Bigram Lattice. Energy order: partial. –Empty, Full, Up and Down. Geometrically: square, two-dimensional.

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http://www.yijing.co.uk Two Dimensions Gua linked together through double line change. These form facets in the complete lattice.

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http://www.yijing.co.uk Three Dimensions Trigram Lattice. Geometrically: a cube. Energy order is partial. –Double the complexity of bigrams.

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http://www.yijing.co.uk Three Dimensions Gua linked through triple line change. Creates cubical sub- groups of hexagrams. The bottom three lines are changing. –Changing different lines creates different substructures

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http://www.yijing.co.uk Cubic Substructures

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http://www.yijing.co.uk Hexagram Lattice

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http://www.yijing.co.uk Structure of Reality Hexagrams: 6-D representation of reality. Complex when taken as a whole. We cannot see the whole all at once. We each have a partial perspective. How to represent different perspectives? Using substructures…

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http://www.yijing.co.uk Subspace Analysis One of 16 facets with the centre two lines changing. These can be linked together into a chain… Local perspective realized as a subspace of the totality

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http://www.yijing.co.uk Unfolding Reality: Introvert Unfolding

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http://www.yijing.co.uk Planar Unfolding Extrovert Unfolding

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http://www.yijing.co.uk Summary Each individual view of reality is partial. Perspectives arise from focussing awareness onto particular domains. Implemented in the Yijing: –Hexagram lattice as totality, –Unfoldings give partial perspectives. Sound mathematical basis.

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