A new Perspective on Dichotomies in Socionics - Pyramid Diagrams, Draft

[Lao Tzunami]

To be honest, it sounds like you are throwing around math terms without fully understanding them. I can see that you understand how to multiply dichotomies but perhaps you aren't too familiar with group theory and formal proof methods?

Well I'm not a math major, but I have taken linear algebra, which includes formal proofs. But since I have not written a proof in a while and have not taken a modern analysis class, I would appreciate the expertise of someone like yourself. The head of my colege's math department has agreed to help me some with this, but she is pretty busy, and I'd like to figure out as much as I can by myself. There is also a knowledge barrier since she does not understand socionics yet.

When it comes to "physical" theories (theories that apply to the real world, that is) the notion of "proof" is a bit hazy -- what is an assumption/axiom and what is derived is usually subject to some choice. Once a consistent model has been presented it's just a matter of working out its structure.

I have two end goals for this project. First, I would like people to be able to understand how socionics works on a fundamental level. Second, I would like to apply the structure with statistics, which would help with empirical research and could be developed into a diagnostic test.

I am a bit puzzled why people want to somehow "prove" that the socion is actually abelian

My motivation is I see a very simple way to put socionics together as an abelian group which I think almost everyone can grasp. I also think there is a beauty to simplicity.

The dichotomies are abelian and the intertype projections are abelian, but I agree that both together are not. I haven't fully thought about this problem, but it can easily be solved by dividing the rational types from the irrational.