Yes, thanks much for the links, Racecar. I read one and was looking at the other one also. Sorry if we're drifting some off topic (but "Everything" is a very large subject and tends to drift
)
Well from the direction I've been pursuing it would appear this would be describing a structure with either 9 or 10 attributes and we should be able to factor either one of these into either 3*3=9 (which would be the equivalent of two parallel 3-way symmetric spaces) or 2*5=10 (as a 5 way symmetry of dualities).
I tend to associate 3 with physical space in terms of 3 dimensions (but adding time makes it 4 and we have motions (which implies 1 dimension of time) both forward in backward in 3 space so that could relate to 3*2+1=7)
But the manner in which I'm using these numbers is not very compatible with an extended linear view of time and the version of time I'm thinking of for this is just in terms of single transitions between two states.
So imagine we wanted to "transmit" information in terms of 1 of 9 possibilities. In this case we actually need one extra symbol to assure we can always synchronize transmissions with a change.
So let's say we just took the decimal digits 0 to 9 (we could also select a vertex of a geometric object with 10 vertices) and then any
transition between 1 of these 10 states is a choice made between 1 of the
remaining 9 states (we can't select where we already are).
And then we could similarly "deconstruct" these 9 as a pairing of 3 way symmetric objects, such as triangles or selecting a line (not a line segment which can point in either direction) for an x, y or z orientation in space etc., but each of these lines would need to be distinct and not interchangeable or end up only having 3 states defined (as the missing 1 of 3 dimensions), so it could be a pair of colored lines intersection at a point.
But in the context of 9 way "wave" motion, I'd assume this would most likely be analogies with a motion on a surface in 2 directions, say x and y, where the velocities could be -1, 0 or 1. This gives 3 possible velocities in each dimension and that's a total of 3*3=9 possible "motions" (one motion is staying still).
So, as an example, we could convert a motion along a 10 sided solid:
http://www.iaw.on.ca/~jspirko/download/primitives_caps.jpg
and any change in its value could be mapped to a single motion (that also included standing still) on a 2 dimensional "matrix".
There are many other examples, but that's just to give an idea of the basic forms of relationships I've been trying to work with.