Friday, July 29, 2011
Surus Cubes L. Edgar Otto July 28, 2011
A good theory and its language like characters in well written fiction takes on a life of its own. We are thus able to reach further than our abilities until we grasp hold of ideas, of motes of light and dust, of the skies. Perception, Foucault, is not necessarily semiotics, and the darling generalization of the day Ken Wilbur, finding a greater unity or not, is not the ultimate essence of God. As with postmodern inter-subjectivity, where we find Wilbur's quadrants times the trinity of Goodness, Beauty, and Truth- thus the twelve, nor more than quantum mysticism in search of the meaning of consciousness can such intelligible mechanisms contain the whole. So beware in the finite realms, although it seems to be compelling in humanity to transcend to godhood in the theory or society of the day, that these quadrants of square circles is not quasic mysticism either.
But I present to you today the Surus Cube (named after Hannibal's favorite elephant that survived crossing the Alps). In that things in quasic space are not as rigid as say any of Wilbur's quadrant philosophies of the I and it, we and collective society times what is internal or external, we have to ask how rigid is the intelligibility of all the mirror images of the eight resultant octans. The paper illustrated above is rather complex while looking for the right ordering of things but this simple cube puzzle goes far to make the more complicated ideas apparent. For while we can divide a plane or cube like this and hold the plane or brane (I should find the first axiom of such space) as a matrix or notation the subsections of that matrix may not be rigid in that they may also turn and twist- certainly like a Rubik's Cube with its Bucky Fuller inner mechanism.
(Two lines intersect into two points?) (If two lines intersect in a point they can intersect two higher space planes?) Maybe a better mathematician than I can narrow this down a bit.
Before this direction of the posts and theories I woke up from a dream of sorts in which I learnedly observed a cube with its colors and complexity so could see it from all sides and could go around it- and when seeing through it at the order of some colors on the other side I did not have the problem of occasionally confusing the face if facing me with the appearance its order was reversed- sometimes just as with sloppy lettering many such twisting around can be hard to keep track of if you are working fast- let alone decipher what you scribbled earlier. But this was not an intense visionary earth-shaking world-changing dream, just a sort of routine I am used to like Descartes to dwell awhile upon awakening.
Still, the question is why in these representations of three space do things have an intelligible ordering and direction - what decides the asymmetry or arrows? What moreover decides the reduction of this deeper information from higher spaces to the paths to get the simpler shadows. While Wilbur shows the errors of holography alone as the theory of everything so claimed by his review of authors not relying on the given alone, that is the monological monism (technically not a criticism of science as much as subjective and inter-subjective, modern-postmodern social issues: I did read his more integral method joint written book last night and I do rather accept his criticism of what is Buddhism as it blossomed in new age America as not quite right, but some things, spiritual things, have now a more scientific basis such as meditation and often a materialist one at that) verses post-modern pluralism.
So, as far as it goes on all levels of this ex-dishwasher's spectrum of growth and awareness (yeah, before I was a candle maker I was a dishwasher too!) his does aim at least toward a unity of diverse if not total incompatible politics and philosophies (especially I wonder if this is possible by those in the pre-modernist mind set who have a tenable position in no way backwards but especially conflicts with post-modern societies now that the modern monoliths like Marxism has fallen.) That in the holonism of the four quadrants he, as far as it goes, expects to inspire the seekers and perceivers to be aware of this level of spirituality. Let us hope in such an appeal to a relaxed unity we can inspire some to a higher level of science too.
It may be of interest that my encounter with Wilbur was more from his first book in which his tenets of Buddhism were a little closer to the original philosophy and mathematics than some popularization as a systems of spiritual practice of which half the draw and power is the ambiance and special rules and language.
The idea in the Surus cube is that from the 64 or 27 of three space (as a four dimensional representation) into the 16 or 9 of two space the structure of the 24 plue 3 colored units is preserved and the orientations are easily seen or implied.
For example in a 9 x 9 array we can imagine particles of three rings of layers as discs- this sort of thing continues naturally to higher spaces. We note that around the 3x3 soma cube in one of 8 corners to view or shift the remaining cubes of the 64 form 7 sets of 5 cubes (after all the pattern is quasic and symmetrical of the six given colors. We can of course extend the symmetry and combinatorial problems by these color changes alone.) Such a "condensing" calls to mind the current tables of the fundamental particles of quarks and such... which with the natural shadows needs not be limited to the standard theory of say 24 or 25 depending on what spaces we regard as rigidly centered.
I have chosen the my standard notation of color LHC on the ordered axis, that is yv,ob,rg and black for the three across one of the Soma cube diagonals. Note that in the Surus Cube these colored center cube faces of any of the outside 6 of 9 are in a sense invariant. But we can invert these. Still in the various versions of this puzzle we note that it has a symmetry as if a ring around an axis- vaguely suggesting to me something like aromatic orbitals and so on in such spatial tori like structures as say that around stars.
Now, in the illustration I will post at then bottom of this page I will color the first octant with the r y o and the g b v in the eight octant. But this does not have to be the only case. The interesting thing about this cube puzzle is that when turned some pieces can be made to vanish or if appear be jumbled into what seems the wrong quadrant in a face. In fact as in my bkd gin color theories we can hide the g b v colors from view always as we twist and turn the puzzle parts. I offer this game only for the addicted to such recreational puzzles and for those who may want to study these types of symmetry problems- and for our addicted mathematicians and computer wizards a good exercise as we extend it to still higher dimensions.
* * *
If it can be done, a clear version showing the octant cubes would be pleasing.
* * *
* * *