Supervisor / Benefactor lattice

[ncassidy]

The following is slow reading and I'm aware of that... sorry that I couldn't revise it to be any less tiring!

Supervision comprises a group, in a loose sense...
- Your supervisor's supervisor is your superego.
- Your superego's supervisor is your supervisee.

As does the beneficiary relation...
- Your beneficiary's beneficiary is your superego.
- Your superego's beneficiary is your benefactor.

With each group containing four elements, and two in the intersection.

Then, what if we take these two groups and combine them, such that it is possible to construct a path between any two people exclusively through the use of supervisor/supervisee and benefactor/beneficiary relations?

We find that the dual is the supervisor's beneficiary and the contrary is the supervisor's benefactor. Surprisingly, the dual is also the beneficiary's supervisor and the contrary is the beneficiary's supervisee.

The lattice traversed by the two relations contains eight types, no matter which type you start: Identical, dual, supervisor, supervisee, benefactor, beneficiary, superego, contrary. It has the following pattern:
[table:a351a15b01]
[row:a351a15b01]INTP[col:a351a15b01]INFJ[col:a351a15b01]ISFP[col:a351a15b01]ISTJ
[row:a351a15b01]ESTJ[col:a351a15b01]ENTP[col:a351a15b01]ENFJ[col:a351a15b01]ESFP
[row:a351a15b01]ISFP[col:a351a15b01]ISTJ[col:a351a15b01]INTP[col:a351a15b01]INFJ
[row:a351a15b01]ENFJ[col:a351a15b01]ESFP[col:a351a15b01]ESTJ[col:a351a15b01]ENTP
[/table:a351a15b01]
It contains exactly half of the types in each quadra, temperament, Reinin dichotomy, Gulenko communication group, and Gulenko erotic attitude group. And of course, half of the Socion. It is a tangible representation of the relations that take advantage of social and economic power.

Note in particular that you and your dual are on an "equal plane" in that the type that has supervision power over you also has benefactor power over your dual. Whereas your contrary has supervision power over your benefactor (two levels above)... and also is the beneficiary of your supervisee (two levels below). No wonder the two can't get along, they can't decide how to properly order things.

On the other hand, I have seen people mentioning some sort of generally unaccepted theory that contraries make good relationship partners. Perhaps just being on the same supervisor/benefactor lattice leads to an interesting interpersonal relationship with all sorts of excitement?

Anyways, what I suggest you take out of this is the following hypothesis: Dual and contrary relations might be seen as two-stage asymmetric relations... with the former "balanced" and the latter not.

For your reference, the other group is:
[table:a351a15b01]
[row:a351a15b01]ESFJ[col:a351a15b01]ENFP[col:a351a15b01]ENTJ[col:a351a15b01]ESTP
[row:a351a15b01]ISTP[col:a351a15b01]ISFJ[col:a351a15b01]INFP[col:a351a15b01]INTJ
[row:a351a15b01]ENTJ[col:a351a15b01]ESTP[col:a351a15b01]ESFJ[col:a351a15b01]ENFP
[row:a351a15b01]INFP[col:a351a15b01]INTJ[col:a351a15b01]ISTP[col:a351a15b01]ISFJ
[/table:a351a15b01]
And it contains all the types that you have a symmetric relation with: Activity, mirror, look-a-like, illusionary, comparative, semi-dual, quasi-identical, and conflicting.

[FDG]

Well, what's the conclusion? Yes, if you construct a polyedra with the types as vertexes and the relations as edges, you can see that the relations of benefit and supervision conduct to your conflcitor in two edges, but so does the relation of conflict in one edge. What I want to mean is, that even if you can construct a path comprised of only two edges, there is always going to be a more advantageous path which only consists of one edge; if you want you can say that edges are vectors with the values of the relations and if you mutiply the vectors that lead in two vertex-movements to your conflictor (edges represented by relations), you obtain the values associated with the edge of the conflict relation.

[ncassidy]

Nothing really, just put it out there The closest thing to a conclusion is just above the second table. I find it more of a useful tool for visualization than anything.

[Mea]

Nothing really, just put it out there The closest thing to a conclusion is just above the second table. I find it more of a useful tool for visualization than anything.

Eh. Yes it is. It's pretty easy to view the relations of the types from those tables.

[ncassidy]

The thing about that is that conflict comprises a group with only two elements, which doesn't provide for any sort of larger-scale dynamics. This neatly splits the Socion in half into mutually exclusive groups which are closed to supervisor and benefactor relations. Maybe fields. My abstract algebra is inexcusably rusty.

It is not really a polyhedron, because the graph is ordered. My supervisor is not also my supervisee. Lattice is a horrible word too, mathematically speaking. It's more like a plane in a three-dimensional type-space. No, that is an equally poor way of putting it. Maybe it's just a directed graph that can't be shown neatly on a two-dimensional page. Yea, that might work.

[FDG]

Yeah I see, you lessen the restrictions and make the group bigger to observe the dynamics between the components. Would be nice to see how the dynamics vary given the variation of a distinct restriction of whatever kind.

[ncassidy]

Each of the two structures can be represented as a torus-like polyhedron (I'm not sure if this is technically allowed for polyhedra, but allow me to take the liberty)... if vectors for supervisor and benefactor relationships are then drawn on the edges and types placed on the vertices, they can be arranged in such a way that no vectors will cross. Similar to combing a hairy donut, which is an analogy I'm sure you've heard before.

What sort of restrictions do you refer to?