Today we will attempt to discuss the Topological Algebra of social co-boundary definitions. We have already looked at the "Dyad." This most primary of social groups can also describe the self separate from an individual group, self to groups, or group(s) to group(s), as long as they are defining two separate "subjects." But when we get into the topological algebra of more than any "2" separate things, (groupings) we are dealing with a much higher order of boundary relations. I will spare you the deliciously tedious geometrical configuration notation for combinatorial spaces where we count vertices as well the edges of lines connecting each vertex. (Big words, simple ideas.)
In doing couples counseling I often have to do the math of identifying both people as individuals while respecting that third entity of their shared relation. "The family is a delicate flower and it must be preserved at great cost." When "I" am talking to you, you are the center of my universe. (Sorry, that's a personal challenge of mine and it is why I much prefer public speaking to say group therapy, or worse yet board meetings.) So when I'm with a couple, I feel I'm switching back and forth between two completely different personalities in me. Talking to that couple inclines me to want a singular identity. I've had to do the math and see the absurdity of wanting to reduce multiple people to closed groups, no matter how conventional. As mathematical relations modeled on co-boundary chains we can think of individuals as vertices forming a central point for the intersection. (Where "i" is the enumerative index. Sorry, math joke.) But we can also turn our social model inside out and start with each of the individual dyad relations (lines of connection) as individual vertices themselves. (This is because each individual relation is discreetly enumerative, but this is descriptive of that singular line of connection forming an edge boundary for separate planes of inter relation.)
Some simple groupings can be mapped onto flat closed networks. But in this kind of 2D model, once you add a 5th entity to a model must take on a higher order of space in order to avoid crossing the "Edges" of these individually countable unique relations in an otherwise flat graphically insufficient 2space.
Although when "God" presides over the joining of two people in this sacred marriage union, we still must respect the "Discreetness" of all people as individuals. Same for all family members. And separate people in groups. No matter how tightly we pack our "Groups" we are still talking groupings. I've had some of my greatest challenges come from disentangling these "Groupings" issues. I would like to go into the covariant and contravariant notations for mapping co-boundary triangles leading us into these higher orders of co-cycles in relationships. But not only does my blogger not handle fonts for boundary chains, I know that the subtle but also potentially apparent dynamics of relations don't need over examination, at least not here.
({r=2sin2phi*sin2theta*sin(phi)} Is the parametric equation I used to demonstrate subjects in spacial relation. Each of the graphic models are different angular views for this same expression. Four like subjects projected into a 3space, demonstrates the limitations of 2d networks for mapping more than three things in relation to each other.)
