Monday, November 15, 2010
Technoflange Arithmetic in the Fifth Degree
Technoflange Arithmetic in the Fifth Degree L. Edgar Otto 11-14-10
[Coffee shop computers down today, posting from library] I continue to have stray insights on the utility of this arithmetical view. It starts with the idea of how we regard the viewing of a surface or plane- there are several ways to set up a design of it, Euclidean, Whitehead, Complex, Lorentz group, Vectors and so on... In this sort of quasic view as applied to real life situations the techneflangelation applies well especially to the codes of life. We quite imagine the plane with various curves drawn on it as if held vertical we can actually represent something falling go a ground. Of course regardless of orientation the ground as the earth itself is rarely if ever absolutely flat nor are its peaks and valley always an algebraic sum unless we assume that over the cosmos but something hard or impossible to prove.
The gist of my proposal today in the literal reading of the quasic plane is that there is another direction to consider- for now I call it the height or q-height. This is not to confuse the idea with depth or span of regions in a quasic plane.
The holon model as other logic or philosophically interpreted models is rather like a window with four quadrants (for example Ken Wilbur's philosophy). But structurally it is an intelligible structure where the rim and flange (and it does not matter which are to be considered the outside of the structures, which is the skeleton and which the content of a subcell region- that to be further explored) that resolves to five squared. Again, this process may not hold beyond a few first levels and this general idea is about conceptual and physical constructibility of various geometrical objects.
But five and its symmetries are intrinsic and periodic to quasic space. For example in the field of 64 regions like a chessboard we can number the cells (in quasic ordering) such that the 25th cell represents the initiator codon in DNA and from the other direction find the terminators around 37. I ask then what is the underlying property where it has not really been considered before. The lower two cells are distinct from the upper two in the sense of more complexity in the Crick bonds of the DNA as perhaps a gain in evolving stability of organisms.
At the lower levels of technorim we find toroidal spaces or space of unfolding orthogonal units as pairs of the first subspace presumably connected in some space if not apparent in this disconnected view. We can alternative regard these pairs as holes in a topological space. Furthermore, from any such cell we can regard the others as containing negative axes of quadrants if not count and volume we tend to ignore. In the lower space we can separate two sub-orthogons as a possibility, but in a slightly higher space the separation leaves points out of the overall intelligibility of the count and contiguity but in an intelligible manner. To map these tekrim orthogons (and the "glue" between them) we have the problem of periodic ordering of things in a quasic plane where the standard orthogon structure is intrinsic to the quasic notation and logic of the quasic plane. If we have two adjacent squares the diagonal between them is the square root of five, from this we derive the realization in two and three space of the fivefold symmetries and in higher space as if five natural dimensions these orthogon-tek differences determine among other things that the cells of an organism (mammal) beginning just beyond 32 is and individual and not a set of independent possible clones. In space of course the flange and rim, log and harmonic. differences move up in the Pythagorean numbers to faster convergent or divergent irrationals, as if we start with the square root of 6, 10, 15 and so on... It has always seemed to me that in an intelligible way to classify the groups that the fact of the cyclic group is listed as an infinite case stands out suggesting a deeper theory for a totality- why the exceptions?
I add consider this as an equation where the integers represent natural dimensions:
(1 + 3) = ( 3 + 1 ) = ( 2 + 2 ) each to the nth, and = 2 squared and so on... when we are asked to choose one formalism or another when all are possible and intelligible and in a primitive right left sense there seems to be an idea of chirality when we simply add things as operation.