The Mapping Formula

The method of representation described below maps 64 6-dimensional points to 27 3-dimensional points to form the I Ching mandala. For our present purposes the operations involved in derivation of the mandala can be considered to be simple addition and division.*

Recall that hexagram lines are traditionally counted from the bottom up, so the lowest line is considered line 1 while the top line is line 6. It will be helpful in understanding of what follows to review previous posts here, here and here. The 3-dimensional geometric placement of any hexagram is determined by adding the numerical values (+1 for yang lines; -1 for yin lines) of lines 1 and 4 and dividing the sum by 2 to find the x-coordinate; of lines 2 and 5 and dividing by 2 to find the y-coordinate; of lines 3 and 6 and dividing by 2 to find the z-coordinate.

These 3 coordinate values specify one unique 3-dimensional point. However, 1, 2, 4 or 8 6-dimensional points (each identified by an unique hexagram) will be found to occur at various 3-dimensional geometric points in the 27-point mandala in the manner described here. It should be noted that this configuration is actually a probability distribution of occurrence of 6-dimensional points in 3-dimensional Cartesian space which is destined to play a significant role in what follows. 

As the I Ching mandala evolves through time as well as space it is not only a geometric model of 6-dimensional space but a simulation active through time as well.

*Later we may have to reassess this stance to determine whether the actual operations involved might be rotations in various of six dimensions. But the simple approach of using addition and division operators does in fact work and will be used for the time being and perhaps indefinitely.

© 2012 Martin Hauser