Friday, January 14, 2011

State of the Vision

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State of the Vision
Friday Post Jan.14,2011 :

I made a comment in reply to Ulla's on Kea's Blog:

Facebook status:

L. Edgar Otto
Yesterday, for awhile, simple addition of some rather weird numbers kept giving wrong answers on the computer calculator. One thinks they are pressing the wrong buttons or something, over and over. But it was a strange idea to imagine a fact- computer compression not like counting pebbles but something hidden in the program itself and its algebra- not like the simple error dividing by zero.

But the illustrations not good enough to post, [due to length I will post this as a new post anyway- and it took awhile for the calculator to work out fewer and fewer errors] although the numbers worked out. It raises the general question that in the simplexes of (1+1)^n we can describe the possible chess motions from the corner of some dimensional board and in the orthogon (antiorthogon) of (1+2)^n motions from the center of cell in all directions. In terms of this abstract quasic motion what then would (1+3)^n mean and why are they so much higher numbers. But the scope of such motions makes me want to take a breath and search out the layers and the normal notations to mull over ideas before further posting along these lines.

In general there are factorials one way and powers the other way to consider. Does the picturing of such numbers aid us in understanding the arithmetic more closely as to it applies to various geometrical representations or the numbers by such pictures?

I will include a rough attempt to post one of these (more and more I see as crude attempts) paintbrush illustrations just as a sample to show I may be overextended in trying to keep things separate as if I myself need a thousand hands (or maybe 2, 6, 20, 70 and so on). Interestingly, sometimes the grueling work of counting and checking puts a break on the smooth flow of speculation- but not something to disturb sleep if you fall asleep thinking about them (as in the early days of thinking about all these rules of addition and multiplication such concentration left me in a grumpy mood the next day.):

As I said, even if the ways we calculate some things is not so certain- I mean our faith in the old 1+1=2, and this an error in the doing it, I can still imagine a situation where a sort of shifting division by a shifting zero in the steps of programming equations, a slice on the echos of levels not that carefully close to the entropy of nature herself confused and defaulting to lower numbers at an original and fundamental decision between alternatives rare in computers. But who knows? Perhaps, there was a shift and briefly, as if part of our creativity and excitement to see and grasp some idea as significant, we briefly felt an alternative and parallel universe?

Which brings me to the quasic chess model again- for the longest time I saw it much like the Hillis Connectivity machine (before that sort of use of chips called that) and suggested it as a way to help the heat problem to Steven Chen before IBM bought his group and this then became a sort of parallel processing for super-computers. I suggested it to my congressman for the library of congress- which was shortly declassified by Bush Sr. thereafter and said for the reason of advancing business with the technology. I received no reply from the senator.

Again, one does not have to communicate and idea (as if the sprouting of violets often said of the non-euclidean geometry and I think the enumeration of crystal groups) for some shared awakening of our current creative wisdom. One has to think the original in the first of a multiverse. But do we so create the idea or in some sense do we foresee the idea- this still the stuff of philosophy or psychology?

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So, although the post of Ulla's comment is a little further back- this question of the significance of 24 or 20 comes up, at least when we ponder the possible mechanism and topology of the gene code. Even the Chinese had a hard time dividing the 64 by 3 of the I Ching- and certainly the duality (or what amounts here to n-(central)ality I imagine- in a sense extends the possibility of paths in such abstract logical space such that someplace they can be connected in logical paths. Vaguely, as all raw first intuitions from a cloud of thoughts that by nature and by interpreting a dream we crystallize hopefully into a more unified and intelligible vision, what is this principle of doubling by the juxtaposition of complex spaces other than the simple rule of adding nearby numbers in the layers of these Pascal analogs? Whether it be two stacks of three pennies in a triangle or ten and ten cannon balls to make a regular pyramid (if of course we build from unit spheres from the ground up)?

Again, somewhere in all this ideas on primes we may find as the best place to mine. But we have to distinguish, even if we can imagine some reduction that defaults naturally to n-ality, n-adic notions of scale, which dimensions we are addressing and which of the insight of one more or less in the embedding of structrues. Three dimensions can be seen as fundamental, but so maybe 6 or ten in this view. There are other reasons than duality (twoness) nature organizes into threefold things like generations and dimensions.

The number involving 24 polytope of octahedra, the analog really to the rhombic dodecahedron in a sense, not the octahedron as some authors casually state, 1152 stands out as worth the trying to see how it fits into all this, certainly divisible by 3 to give 384, the double factoral group of the hypercube. But from this can we say that one day we will find in the labs concrete new particles based in such higher dimensional spaces as ten once we really find the proper grounding of these limitiations and notions? Can they be made artificially once we understand nature?
In any case the dual honeycomb, be it the old hexagons and triangles, or the cubic lattice and the mixed tet and octahedral lattice- this is the 20 and the 24 in their relationship. I do not forget that not all cells of some closed orthogonal boundary of something like the chessgames are in the corner or floating freely somewhere on the board. Nor in our vague notions that the very idea of a bounded or isolated board is an ambiguous question that may vanish when resolved- where it may not matter if we view the connections of abstract motion, even ideas of spin and force, as merely a simplex group or an orthogonal group in whatever definition of dimensions. Again, strings in concept may not be clearly open or closed.

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This article seems very relevant to the method of taking hints from nature as well as our design of logic systems:

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