This post is about alternate coordinate systems, in addition to the familiar Cartesian system, where each axis is at right angles to every other axis. The terminology I use is xMy where x is the number of axes and y the number of dimensions being measured. Cartesian coordinates are 1M1, 2M2, and 3M3 in 1, 2, or 3 dimensions. There is a 2M1 system, a 3M2 system and a 4M3 system in which all the coordinates add to zero for any point in space. 2M1 is simply a standard Cartesian single dimension paired with its mirror opposite. 3M2 has 3 axes oriented on a plane from the center of a triangle towards its three corners (or towards the centers of its three sides). 4M3 has 4 axes oriented in 3D space from the center of a tetrahedron to its four vertices (or towards the centers of its four faces). Here is a graphic representing the 3M2 system.

3M2 Coordinate System

Coordinates are given in the diagram for points p, q, and y. Point x is precisely between p and q – hence, its coordinates can be determined by averaging the coordinates of p (0,3,-3) and q (2,-3,1). So x is at (1,0,-1).

There are three different versions of 6M3, which I identify using a subscript to the 6, and which I will write here as 6(0)M3, 6(1)M3 and 6(2)M3. The first of these, 6(0)M3 is a doubling of 3M3, each axis pairing with its mirror image. 6(1)M3 has axes oriented from the center of a cuboctahedron (Bucky Fuller calls it a Vector Equilibrium) to its vertices. The 3M3, 4M3, 6(0)M3 and 6(1)M3 can all be easily lined up with the tetrahedron, octahedron, and cube. There are more complex systems, 6(2)M3, 10M3 and 15M3 that line up with the icosahedron and dodecahedron.

Kirby Urner has a different take on what I call 4M3. He named his form quadrays. More info on this can be found at www.grunch.net/synergetics/quadrays.html.

He uses the term “micro-chakras” in the context of human development. Each of the seven (major) chakras has within it a sort of miniature version of each of the seven chakras. These 49 stages are further divided by the three major nadi-s (or channels – left, right and center – named ida, pingala, and sushumna respectively) through which they manifest, forming 147 micro-chakras. The micro-chakras take center stage in turn as the human organism develops. In the first year of life, energy goes down the right channel, then takes the next 42 or 49 years to go up the right channel (6 years per chakra for females, 7 years per chakra for males). Trauma in one’s life can form blocks in the then-developing micro-chakra.

I see correlations with this model of human development and Abraham Maslow’s “hierarchy of needs” (no reference at hand). We start with a need for grounding, security (first chakra), then for relationship to family and friends (second), then ego and power (third), unconditional love (fourth), and so on.

I recommend the book Chakras / Energy Centers of Transformation by Harish Johari (Destiny Books, 1987) for extensive detail on the chakras and their meanings. It refers to the topic of this post to some degree in the descriptions of the “behavioral characteristics” of each of the chakras.

I (and many others) know Harish as Dada (“older brother”). He wrote many other books – on yantras, breath, ayurveda, Hindu myths – some child-oriented, massage, cooking, gems, numerology, and more. He was a master artist. Among other media, he used layered watercolors with washes between layers. He drew from classical sources to express the gods and goddesses that were often the subject of his paintings. His voice is available on CDs and other media.

Dada and Shyamji have sung sounds that can carry the listener to rarely-visited realms in the seas of the chakra energies.

Some of those who were close to Dada formed Sanatan Society, which has .org and .com web sites.

Publisher Inner Traditions has produced many of Dada’s books, and in 2009 a book by Shyamji with co-author David Isaacs, called Microchakras / InnerTuning for Psychological Well-being [Includes CD of InnerTuning Sacred Sounds].

I have Shyamji’s book. I find myself unable to listen to the CD, nor delve into the text, for personal reasons. However, I do believe its description of [ the components of the being known as "human" and their development through a life ] has great value.