Wednesday, July 28, 2010
And, Or, & And-Or
And, Or, & And-Or
Today I am just intuitively exploring some aspects of space and am not sure if things like it exist anywhere. Just as the most difficult last post it comes from casual and random exploration of an idea- simply to find some variation on chess games that may not be as complicated as my n-dimensional ones. This fascination philosophers have with the dice and their symmetries is at least good as analogies to how we see some physics ideas or how we may from this study find new ways to see physics.
As you see in the illustration the 16 chess pieces are arranged on the 61 cell board such that the knights and bishops start from different colors. After all in the case of the bishop the parity does not change, and in the case of the knight it changes regularly and alternates on the whole as a balanced parity (that is color of the squares).
Furthermore the queen moves are an either or proposition of motion, and the knight moves which covers what the queen cannot is a and or situation. The main diagonal of the Conway matrix area in the case of this board is turned 45 degrees to make it the edges of an 11 by 11 lattice of squares. In a sense this is the limit of physical things if we are to regard 11 as the knight shifting density number in five space. How we see five space is after all not that more complicated to draw than four space if we keep the dimensions clear as to our vision and notation.
In such an 11 x 11 board we have the properties of the color alphabet which suggests to me an idea of the light cone only a more discrete version which includes and gives meaning to the imaginary color space outside the light cone. Now maybe the shift down the main alpha-beta diagonal has to be assumed moving and thus a form of causality. Maybe this directionality arises from the properties of the cone, or maybe- which in this case I doubt it by definition, that property of the fact of three space and one space. But in a sense with the proper ordering we can see even three space as a linear one space.
We imagine then the 9 queen problem as an orientation of some cube (and for all such theories involving orientations in some space). From any one queens local perspective and or or, it fills the space and in a sense much like the directions of cells on a surface of a polyhedron these are the shadows thus number of dimensions the symmetry is involved in.
But it is not clear such ideas of orientation and parity apply beyond some space- I mean it is one thing we need the proofs of so to find the variation on the notions suggested. I feel it does apply. Given this my alpha and beta quasic time directions plus the general distinct but similar 11 orientations we find an intrinsic difference in these times as far as the expression and unification of these orientations go. We know when this matrix and its methods of expression are mapped to the genes that there are distinct and I feel topological differences (which as Rowlands points out) involves chemical bonding numbers also- that is beyond the 2 or 3 or even the hydrogen bonds.
There is in a sense a quasi- or partial symmetry breaking- and thus a quasi breakdown with direction of some of the conservation laws short of complete annihilation. There is moreover against a dark background of contiguous phenomena a connection between those cells of one type of particle and the other in the sense of parity across the directed quasic Conway field where the state of things despite indefinite temporariness persist and most likely on the whole as to be measured as positive with a measurable chiral difference because of the discrete arrow of time and the quasi mirrored location of complex points which in a structural design sense my distinguish unto some dimensions of mathematical properties the sign of things (nature then perceiving much as we do our symbol system intelligibility.) In a sense this arrow is one of mass as well as any flow of signal energy. There is an analog of the inverse square law and space but in higher dimensions than just Kant and Newton's sense as a fitting intelligible design and reason of being for that law not necessarily in a non-linear sense even if the roots and squares are taken, and we do not lose this balanced obvious relationship with orientations, dimensions, and that property of inverses represented so well by complex analysis equations (albeit they are incomplete in the interpretation of physics at the foundation.
Then again this is an early insight of some sort- much like how it began with the four dimensional chess and thinking of some sort of inverse picture of the inverse square law.
* * * Idea left out earlier:
From the algebra there is no way to show the sign in complex space so yes we may interpret duplication of such spaces as far as intelligible numbers of dimensions go. But there is no good reason to assume such duplication is symmetric but can be quasi-symmetric such that there is an intrinsic difference in the parity, chirality, time, and charge conjugation so interpreted as physicality from topological terms alone as this field model above seems to suggest as a possibility- not even when all things are reversed needs the idea of symmetry as mirrored be balanced the same- yet this needs only be observed as imbalance on deeper and rather opaque levels than we in direct experience of the behavior of particles in either or both aspects of their definition in some space or time as continuous or discontinuous.