## Wednesday, June 23, 2010

### Passport to Platon (Kocham Subsymmetries)

Passport to Platon (Kocham Subsymmetries)

I took photos of the last two pages on this strange idea of symmetry in Kocham space as quasi-objective entities. Sorry for the curved or missing notes in the margin. Using the quasic grid ordering and the dimension of color one can represent the variations on things in a cube by the color- and here I envision three or four generations of kocham particle systems (these structures are orthogonal linkoms and binary regulus points and natti points for the idea of scale and dimensionless scale and real or rational numbers. (certainly Whitehead's alternative to relativity did work initially on such a foundational level with ideas of congruence and stretches and implied complex numbers.)

Imagine then the rotations, as if these are after all double factorials thus the groups of rotation and inversion of the orthogons of a given dimension, can be represented as a coloring of the quasic grid elements.

The Kocham particle is composed as a cube of some dimension and as part of a wider cube of which the remainder of cells is a difference of cubes. In a sense this is a combination of holographic models. Thus we see 8 for a single cube, and 24 for a 3x3 cube and 192 for a four dimensional cube and 1920 for the fifth degree case.

In a sense we have lain the foundation for the reason of being of the Pythagorean Theorem and it follows the cube relations as subvalues limit the range of the structures to a given dimension- that is in this limited infinite descent we understand the use of the term cube by Fermat better as he saw space or algebra so that in a sense where things are foundational they are also elementary proofs of Fermat's last theorem. Certainly 3 cubed plus 4 cubed plus 5 cubed equals 6 cubed is an intelligibly arithmetical quasi-objective thus quasi-physical equation.

What this implies in the case of five dimensions is the validity of the logic of the relationship of systems (now thought to be non-linear only) such that for the five dimensions we can envision factors of ten as in DNA stacking and the 120 cell as if 5D matter. Here we rotate things in higher kocham systems of orthogonal space. But in a real sense the translation and rotation meet in these structures and are intelligible between the counting of the dimensions.

Kocham!! (double factorial) systems

* An intelligible design system may appear as if its (subkochamic) parts inter-communicate (as if on various generational levels such as organic cell proteins or codons or chromosomes and so on). Thus the ambiguity between structure and messages(messagers) is a coherent (gauge?) changing yet unified intelligibility. There is therefore intrinsic symmetry breaking (and intrinsic asymmetry)and intrinsic unification for a system.

Somewhere between a linear and circular, volume or surface effect is this indefinite signal system.

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