#amplitude potentiality

Beyond Descartes - Part 7

Composite Dimension and
Amplitudes of Potentiality
Episode 1

(continued from here)

Having frightened away all the cognitive wusses with my remark in that last post about the complexity of composite dimension and of the mandalic coordinate system  based on it,  I have a confession to make to those followers who remain. Although understanding the ideas involved requires a step back and viewing them from a different perspective alien to our Western modes of thought, composite dimension and the plane of potentiality are at once  more natural  and  far less complicated  than are imaginary numbers and the complex plane. Stay with me here. There is a light at the end of the tunnel growing ever brighter.

The 6D/3D mandalic cube is a hybrid structure having four levels of amplitude potentiality represented geometrically by 27 3D points which correspond to Cartesian points centered about Cartesian (0,0,0) and 64 6D points,  corresponding to the 64 hexagrams,  similarly centered and distributed among the 27 Cartesian points  in such a way  as to create a probability distribution through all three Cartesian dimensions,  that is with geometric progression of the number of hexagrams resident in the different amplitudes or orbitals. This gives rise to the mandalic form of the coordinate system. There are  four well-defined orbitals or shells  in this unique geometric arrangement of hexagrams and,  parenthetically, whatever it is they represent in physical terms.^[1]

We can conceptually abstract and decompose the 3D moiety of this concept entity, the part corresponding to Cartesian space. In doing so we identify a cube having a single center and eight vertices, all points by Euclidean/Cartesian reckoning, twelve edges (lines), each having an edge center (points), and six faces (planes), each having a center (point) equidistant from its four vertices. Each vertex point is shared equally by three faces or planes of the cube and each edge, by two adjacent faces or planes. We have  previously analyzed in detail  how the six planes of the 3D cube dovetail with one another and the repercussions involved. (See hereandhere.) One of the most important consequences we find is that each face center coordinates in a special way all four vertices of the face. This becomes particularly significant  in consideration of the composite dimension-derived hypercube faces of mandalic geometry.

The 6D moiety follows an analogous but more complex plan and has been formulated so as to be commensurate with the convention of the Cartesian coordinate system.  It also introduces measurement of a discretized time  to the coordinates,  thus rendering the geometry one of spacetime.  The hybrid 6D/3D configuration introduces probability as well through its bell curve/normal distribution (1, 2) of hexagrams; and also,  the two new directions,  manifestation (differentiation) and potentialization (dedifferentiation).^[2] These unfamiliar directions are unique to mandalic geometry and the I Ching upon which it is based.

In the lower diagram above, the figure on the right represents the skeletal structure of the hybrid 6D/3D coordinate system;  the figure on the left, the skeletal structure of the corresponding 3D Cartesian moiety. The  27 discretized points  of the cube on the left have become 64 points of the 6D hypercube on the right.  In the next post we will begin to flesh these two skeletons out.^[3] The end results are nothing short of amazing.

(continuedhere)

Notes

[1] With this remark I am avowing that mandalic geometry is intended not just as an abstract pure mathematical formulation,  but rather as a logical/geometrical mapping of energetic relationships that exist at some scale of subatomic physics, Planck scale or other. I maintain the possibility that this is so despite the obvious and unfortunate truth  that we cannot now ascertain just what it is the hexagrams represent, and may, in fact, never be able to.

[2] Manifestation/differentiation corresponds to the direction of divergence; potentialization/dedifferentiation, to the direction of convergence. The former is motion away from a center; the latter, motion toward a center. Convergenceanddivergence are the two directions found in every Taoist line that do not occur in Cartesian space, at least not explicitly as such.  There are functions in Cartesian geometry that converge toward zero as a limit. To reach zero in Cartesian space however is to become ineffective. That is quite different from gaining increased potential, potential which can then be used subsequently in new differentiations. (See also the series of posts beginning here.)  Both the terms differentiationanddedifferentiation  were  brazenly borrowed  from the field of biology,  while the designations manifestandunmanifest  have been shamelessly appropriated from Kantian philosophy, though similar concepts also occur in different terminology in deBroglie-Bohmian pilot-wave theoryasexplicitandimplicit.

[3] In the figure of the cube on the lower left above there is a single Cartesian triad (point) identifying each vertex (V),  edge center (E),  face center (F),  and cube center C.  In the right figure, the  hybrid 6D/3D hypercube  at each vertex has one resident hexagram identifying it,  two resident hexagrams at each edge center, four resident hexagrams identifying each face center, and eight resident hexagrams identifying the hypercube center. This brings the total of hexagrams to 64, the number found in the I Ching and the total possible number (2⁶ = 64). This geometric progression of hexagram distribution,  through three Cartesian dimensions constitutes the mandalic form. It is entirely the result of composite dimension.

© 2015 Martin Hauser

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