## Friday, July 16, 2010

### The Depth and Span of Fields

The Depth and Span of Fields

I wonder if my curiosity for how the world is made was satisfied long ago - after all is it really that simple that we apply something like the Klein 4 group to variations of quaternions from Dirac, put them on interchangeable vertexes of color on some deeper understanding of the dimensions of the cube? If so, and without formal study even of such groups but of the geometry at the foundations itself I begin to understand on one hand the difficulty of such simple pastimes and yet on the other hand feel keenly how primitive our body of knowledge and methods of analysis are. The cost of theory can far outweigh the boondoggle cost of some experiments (friend Lubos).

Are we entering a new age for such things as dark matter (say applied to the dipoles and helix coherence of DNA) or do some of the New Agers in their parlor games of stealth and chance really work the foundations of concrete physics- in a way the depth of field and the span is after all a subjective matter of taste and as fundamental to the human psyche as Newton finding the corpuscular irreducible s or Leibniz reveling in the infinitesimal. But what is dark matter that it was not conceived long ago along with Black holes from the Newtonian model? And who was this Newton that he considered the non-linearity of particles with their own influence of charge and mass? Or he who saw the philosophic problems of a ever descending explanation of the hierarchy of particles. These philosophers who first thought about zero and infinity, vacua and the roots of things, the calculus.

* * *

Tubing On the River L. Edgar Otto July 16, 2010

Foggy whirlwind devils dance and spin

over the river's mirror and reflected within

Their depth and space dragging directed Dervish

soul that I change directions with my will

Or just that I change my mind's perceptions?

flip the vertex color, infinity the span?

All along the mayflies and dust motes,

fallen leaves and spent egg cases

Seem to spin both ways with the river's flow

upstream as well as downstream seeking levels devine

The further back in time flow to origins

the universe shrinks and its age grows, eternal its measure

Here now I float with the river its glass bottom with

my prying eyes on an inner tube and all is timeless

My brain is full of entanglement on a staircase

yet this too even save in some bubble I doubt as real

Where would I store the ice and rainbows of some

grander design from my dreams to build

Measure my soul against the aether wind of the river's water

even if my dust's nature is still lest than my artful hands?

* * *

The vacuum in a sense has structure (as my 00 and 0 notations, that is the double square roots of things or like in Rowlands proper time and time) such is the roots of zero and one that some entities invisible may assume distinct dark functions and structures. Now three space has its foundational place as well the higher spaces but 153, 670, 671, and 470 as the digits cube equal that number is the example of roots of one or zero that are important to expand the set of such numbers beyond the also included 1 and 0 as sums of cubes in three space.

The quasic dimensional depth is also the natural dimensional span. The ideas of field complexity and compactification meet the "flangelation" in our geometric explanations of order and place, of symmetry and anti-symmetry, of the discrete and the continuous in a dance of spinning perspectives.

Thus in the span in the stillness of the simply connected plane concrete bits of light may move between the curves or between such planes in depth the ghostly particles of dark light move, enfold, and we do not see it directly- nor that these are in some arrangement of fundamental space not separate at all over entanglement.

Why is it hard to accept between choices in our mind that such topological things may be the ground of all we hold physical and then not to accept the "superior sperm" of longevity and intelligence of our species (new scientist article); yet not also accept the same reality of the experienced but also equally metaphysical substance of our mind. I either move beyond or ignore those who choose sides with the consequence of the broken symmetry of war.

So, in the aromatic places of zero probability to find some electron we stack them as if three or four cubes in the rotate then flip - and behold the nature or physis code, the cosmic code, and the stability and reading of it- in the threesome of the 3+1 and even holonic formalism (as all such logic classically beginning with Aristotle and the symmetries of Dihedrons and Klein's least not cyclic group) we derive the possibilities of path motions in the dimensions and between the centered or focused cubes of hyperspace we observe the mysteries of quantum logic. Yet that is but a cloud or fog along the way to new beginnings back to the foundations.

* * *

Another mathematical recreation last night with wide variations, 30,50 stars and so on for a simplified USA flag:

* * *

* * * A Footnote to previously mentioned hints at further topologies applied:

From the perspective of continuity and the world according to Coxeter what is in the actual arrangement of the atoms of the bases are also analogous in a relaxed manner to the general coherence of the space, especially where it is a discrete choice and application between the hierarchy of systems in a relaxed quasi-deterministic manner. Not only the Hydrogen bonds between matched bases an important consideration (and the process of the first star atoms unto Helium) but the actual number of atoms considered at rest mass and yes the isotope numbers that can affect the global field (perhaps the dihedral angles significant here are the square root of 11 plus or minus 1 divided by two and so on... This sort of thing may be generalized as a principle I suspect and should have a more formal treatment of what is going on at the foundations.

But the jewel is perhaps where Coxeter investigates the plane as a polytope, that is his small delta notation which has honeycombs of five such spaces which are their own duals in a cycle of five of them. Such a principle at the frontier of his geometry (in an Euclidean manner) most certainly applies to string like and gauge like theory's. Again, from the quasic generalization the order of the elements in a group may not be restricted to the idea of distance involving the square root of two. Certainly the fourth root of one half as a value for the Lambda with its added pion times the proton value seems to give intelligible and observed measure. The averaging of state values for say the Xi needs deeper than the usual statistical principles I imagine as a working idea it seems enough for now. This five fold-ness beyond the classified cyclic groups of linearly applying the reflections and so on embedded or not in some space sets the limits to cyclic things for a linear dimensional direction where parallel things are coincident. For example a two by two by three unit of cubes and five of them may contain the pentacubes of two space (12) so he intuition of what we can do with these simple cubes has deeper mathematics than we seem to be able to program with our current principles of patter recognition. Also, in fractal paths if we have an implied axis that may assume one of several colors there is no reason to prefer such in color effects on path directions. Of course the principles of symmetry and conservation as with Rowlands can be generalized- I suggest it can be so even further.

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