Tuesday, January 15, 2013

Bogged Down in Higher Arithmetic

Bogged Down in Higher Arithmetic

(Breaking thru the Marsh Gas Swamp)

L. Edgar Otto    15 January, 2013

My two unsolved problems have been instructive for many insights along the way in understanding systems.  The first was my teleoscoping ordering as a linear dimension for the thematic connections between four base codon systems.  In the plane quasically ordered the telescoping seems capable of description by layering of regions in the plane but we know the information in the plane is equal to that as its square root at its boundary.

The second problem was what particular patterns or structural systems exist for projective analogs of color matching cubes and their enumeration into higher dimensions.  I recall this morning seeing the cover of Scientific American where it showed the Graceo-Latin square of ten by ten elements announced as solved, some years ago- I do not know the status of this problem in higher cases but I have already extended my grids beyond that so am not sure how this may change my general methods as if a swamp land (and in the Slavic Bog translates as God, the Marsh an important concept in the Chinese binary divisions, and in our time the idiom or phrase that what we may see of UFO aliens is some trick of light involving the atmosphere or marsh gas).

I am in a strange place off line- having the old coffee shop computer I can get more done at home before the time allowed was taken up by the writing on line or the translation from the old technology- my ink and paper.  It would benefit if I had direct access to Google things as that takes up time allowed thru the access at the public library if I think to look things up- I usually Google my mind first.  The very use of computer programs touches on the methods of these unsolved problems like the trivialities too obvious almost to state, of counting and of pattern recognition.

In the color matching, including the possibilities of those of higher orthogons listing the greater or equal to four axes and the shapes and articulation of folding or unfolding them, this and the general idea of Eddington's fundamental theory concerning the fine structure constant (the quasic idea one of generations of particles thus the one fourth of such an analog to that constant ) , and all the ideas concerning matrices in general or the magic squares, the main diagonals as a merger of colors into groups of neutral gray or vanishings and masking of a sphere or brane region (as if to see the logic of it we need x-ray vision that hopefully does not disturb the ordering of objects observed,
I considered the obvious moving of a quarter of the total grid of so many generations over the compass of all the grid that we align each pixel region (which can be a fixed origin of the quasic plane or a class of branes in itself) to combine the colors where all are present at such a point.  This most likely enumerates the possibilities of color matching but I have not formally addressed all the cases.

In my notation the bi-color letters B O G are red-yellow, blue-violet, and orange-green, which I picked at random for the illustration and it gave me the poetic theme for this post title.  The transparency of the paint program close to the logic allows such logical stacking that concerns itself with those raster symmetries possible of which the staring into the art of it may seem to be concrete or fanciful illusion.  This itself a question of inversion, and the odd way to order things that the inversion of a single axis may invert the sense of all of them if viewed from outside to a symmetrical center.

While I understand the directions of vectors in four space shadows and the 30 edges of intersphere elements for a polyhedron, there is a sense that to understand four space one must imagine having six hands, three right and three left.  Will this method in the illustration solve the problem and should we investigate it further in terms of the information content of the coordinates and definitions, giving us a sense of the unity of the whole ( it seems these problems here solved synthetically as hints and promises is after all key questions underlying particle physics and issues in number theory's that bog many down and keeps the breakthrus cloudy)?

I still get the sense these quasic pictures give us a wider general view of such problems that speeds up and makes easier our application of awareness over the algebra alone to which many are adept as formalism only or not if indeed these are equivalent methods- but there is little doubt that this birds-eye-viewing readily shows us where in the listing of programming or the order of algebra labels the pattern of things so organized and applied as our viewing may readily show us choices otherwise difficult to solve in linear pathways.

I am not sure how this connects to the obvious expansion of the technology, the new HD tele for example apparently in a parallel view of the ubiquitous logic quadruples the HD screen pixel dimensions (does this not come closer to the sense we are in that space in the viewing of things in three dimensions as we adjust our right and left colors of the old extreme, the space of colors for holograms, until it is felt we do not need such unifying or partition of mirrors as they lead the structural organization thru our mind's eye?).

Symbolically, the joke goes as we round off the binary of 2048 to 2K, that the computers crash in the year 2000 but 48 years later (that is if Netscape or Microsoft is right about where to start as the first pixel of the year one or zero).  The question now is with so many generations as a possible limitation of patterns as we build the idea up, will the world end or the computers crash in the year 4096?

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