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Chorand Spheres

Introduction

In this section I describe a construction developed by Henri Chorand which provides an interesting way of orienting the 6-dimensional Boolean lattice in 3-dimensional space. It does this by describing the outer-most surface of the lattice which could be perceived. This is a two-dimensional surface curved in the third dimension, a sphere. It provides a general construction which, for any given starting point, orients the lattice in 3-space, identifying the surface hexagrams as one group, and the remaining "internal" hexagrams as another group. This construction is directly related to the set of hexagrams with an internal energy boundary of less than 3.

  1. Firstly, here is Henri's description of his construction as posted to the Yixue discussion group on 3rd October 2005.

  2. Next, I have created diagrams of the two Chrorand Hemispheres which are derived from the Receptive/Creative axis.  This page also illustrates how their union is topologically equivalent to the ieb < 3 structure.

  3. For each sphere generated on a particular axis, the Chorand construction generates a second sphere on a perpendicular axis. This page explores the sphere perpendicular to the the Receptive/Creative sphere.

  4. It is possible to generalize the Chorand construction using Boolean algebra. This makes it possible to generate pairs of spheres based on any axis.

  5. Penultimately, I return to look at how these spheres project the lattice into 3-Space.

  6. Then some more Sparking with Henri.

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