#commensuration

Placement of the trigrams

  We begin by making the I Ching trigrams commensurate with the 3-dimensional Cartesian coordinate system or rather, showing how it already is before we set a mind to it.

Let the lowest trigram line correspond to the x-axis coordinate (horizontal).

Let the middle trigram line correspond to the y-axis coordinate (vertical).

Let the upper trigram line correspond to the z-axis coordinate.

Let yang correspond to +1 (vector, not scalar; i.e., magnitude 1 in positive direction.)

Let yin correspond to -1 (vector, not scalar, i.e., magnitude 1 in negative direction.)

Let the center of the cube be positioned at Cartesian 0,0,0.

      These ascriptions result in the following correlations*:

      * These correlations differ somewhat from those shown in Quantum Geometry (1, 2, 3) because the orienting convention of the I Ching was used there whereas here the Western convention originated by Descartes is used to minimize confusion. The two are interchangeable by rotation of 180 degrees about the y-axis. The numbers with which the cube vertices are labeled have no significance other than a convenient handle by which to refer to that specific vertex.