Mandalic geometry and polar coordinates - II

(Continued from here.)

SPHERICAL MANDALA (cont.)

Some additional points of significance off the top of my head*:

1-The sphere can of course rotate about any axis, but the axis between   

                              and   

is our primary reference axis. These are the hexagrams situated at the south pole (solid lines) and north pole (broken lines), referred to as Heaven and Earth or Creative and Receptive respectively. If the sphere rotates about this axis the two points defined by these hexagrams do not move. They serve, therefore, as our polestars in the system. [South by convention is shown toward the top of the diagram in ancient Chinese cartography and that is the convention adopted here as it preserves certain essential prepotent associations of the ancient Chinese schema found in the I Ching.]

2-The four shells of the sphere can in a sense be considered analogous to energy levels of electrons in the atom. The hexagrams in the outermost shell are less tightly bound than those in the deeper shells. Binding energy increases in each shell moving toward the center. Binding energy here is related specifically to the number of 6-dimensional points which share or co-exist at a single 3-dimensional point.

3-Binding energy in this context can moreover be equated with the degree of connectivity of a group of hexagrams sharing a point in a given shell. The connectivity referred to here is both among the group members and between the group as a whole and all other groups or hexagrams.

4-The highest degree of connectivity occurs with the group of eight hexagrams sharing the fourth shell or central point of the sphere. These together constitute the point of totipotency from which all the hexagrams in all the shells may be considered to arise. The entire structure of the mandala therefore can in theory be reconstituted from this single generative point. This point is the zero point (origin) of conventional mathematics but in the usage here is akin to the quantum vacuum or the null point of modern physics.

5-It is important to note that we arrive at the polar mandala by a simple slight rotation (in 3 dimensions) of the Cartesian form. The relative positions of all the hexagrams to one another are unchanged. We have just positioned the hexagrams (and the mandala as a whole) in a different but congruent frame of reference. Only our own perspective has changed.

                                                                        (Continued here.)

*Off the top of my head at the moment, but I have been preparing for this moment for half a century.   

© 2013 Martin Hauser