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

I want to emphasize that this is pure classical socionics. I have not added anything new to the theory. These diagrams are simply a tool for understanding Model A, or any other similar model.

I invented these diagrams so the average person can use the dichotomy structure correctly. I'm posting this here to see if it make sense so far and I'll make changes based of your feedback.

Excel Program (now with a Comprehensive Tutorial):
This is where I would start. This excel program is a hands on demonstration of these concepts. It includes a newly completed tutorial which will teach you everything you need to know about type dichotomies, as well as a dichotomy calculator and a working outline of a test.

Please download and open in excel so it can work properly. Enable editing and content for all the features.
https://drive.google.com/open?id=1bp...b9NsdLUoNqMv1i


The calculator:


A section of the interactive tutorial:


New to the latest version, the sixth tab "Random Experiment" allows you create and record random inputs (based on the setting on the input tab). Be careful not to run too many cycles or it will take a long time to complete. I've also included the results of "100,000 random cycles" on the 7th tab, which took me 11 hours to generate and a nice histogram distribution on the 8th tab.


Article Draft:
This is my first draft. I'm still working on this
https://drive.google.com/file/d/1ix_...ew?usp=sharing


Small Group List:
http://www.wikisocion.net/en/index.p...ll_Group_Table


HD Video Model
https://www.youtube.com/watch?v=nEydBdhvhIs
(right click on video and select "loop")

Thank your for your post, I think the diagram pretty nicely encapsulate the relational structure of the reinin dichotomies and how they are connected to each other. I can promote this in viewpoints if you wish?

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Originally Posted by mu4

I can promote this in viewpoints if you wish?

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Glad you liked it. Feel free to post this where ever you want. The more people who understand socionics, the better.

Do you think this is a good enough basis to go into more complex topics?

Quote:

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Originally Posted by sindri

Glad you liked it. Feel free to post this where ever you want. The more people who understand socionics, the better.

Do you think this is a good enough basis to go into more complex topics?

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I'm not sure I understand all of it but some of the things are very interesting to analyze. You've put a lot of work into this so I should put the same work to understand it.

I probably will need to ask some questions about this as I get into it. Some parts of it where you get into typing was interesting but not sure if it helped explain the structure, more application?

I don't visualize the same way as you do but I see something interesting in the way this is being visualized.

You spend a lot of time explaining how you came to these conclusions but I'm trying to grasp what the pyramid represents.

Maybe when I see your multiple pyramid write up I can understand.

Also your ENTP notation is arbitrary, but what does this pyramid represent, and what CAN it represent and how to do it. Can it represent the type? Does it represent model a relations in a "space of" all possible types? If so then does some point in this pyramid represent a type?

I'm not very math saavy but these are things I'm getting from what you've written.

I do think what you've written is thought provoking and attractive, and I hope I'm not totally confused.

I went through most of it. Is there a way to say, plug in different types by default to see what out of two different types one is to choose from? For me this would be INTj and ISTj, so same leading function.

I love it.

having the four main variables map out to four dimensions is very intuitive to me.

I like being able to look at a line and think: "Ahh so the combination of Extroverted/Introverted + Rational/Irrational is what makes Static/Dynamic (and by flipping one of the dimensions you go from static to dynamic and by switching both you just go back to the same". It's not "new" to me in the sense that I know these things, but I usually have to go back to the dichotomies themselves to figure out how they work. This encapsulates a lot of information in a very easy format.

What would be the next step from my perspective is to make a web-tool that allows you to flip the variables into their opposites dynamically so you can just "click" you way through the socion basically.

That would allow for a "ceteris paribus" approach of experimenting while keeping the overview intact :)\


Edit:

and then use highlighting within that 3d model to show the groups and lower level dichotomies like you did in the end of the article.

Making it an educational tool instead of a document would probably do two things:
1. make it much more likely to go viral (better marketing) 2. make it much more likely to get a longer exposure (play is easier then reading).

Quote:

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Originally Posted by mu4

You spend a lot of time explaining how you came to these conclusions but I'm trying to grasp what the pyramid represents.

Maybe when I see your multiple pyramid write up I can understand.

Also your ENTP notation is arbitrary, but what does this pyramid represent, and what CAN it represent and how to do it. Can it represent the type? Does it represent model a relations in a "space of" all possible types? If so then does some point in this pyramid represent a type?

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I haven't read her stuff, but from the pyramid I gather you can make any type into the pyramid by switching the main dimensions (which I'm sure you have seen already).
So the thing can represent the entire socion, but not at the same time.

I think it's basically the four letter notation (or three letter notation) but then optimised for visually oriented people (or maybe HP-cog although op is IEI so....)

Quote:

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Originally Posted by QuickTwist

I went through most of it. Is there a way to say, plug in different types by default to see what out of two different types one is to choose from?

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I think what you are asking is if there is a way to compare two types? Yes there is, here is a comparison of LII and LSI. This is the basics, let me know if you want to see more.

Bottom right are all eight dichotomies you must be to have introverted logic as your base. The other pyramids on the bottom center and left are the eight dichotomies that are different for each type. You are either all of one or the other. If you actually want to determine your type based on these, check out the 2003 reinin dichotomy study.
Attachment 7507

Quote:

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Originally Posted by mu4

...your ENTP notation is arbitrary, but what does this pyramid represent, and what CAN it represent and how to do it. Can it represent the type? Does it represent model a relations in a "space of" all possible types? If so then does some point in this pyramid represent a type?
...
I do think what you've written is thought provoking and attractive, and I hope I'm not totally confused.

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You are right, the ENTP notation is arbitrary, but it is the standard established by Reinin himself in his mathematics and is standard practice for all socionics. This is already complicated enough, so let's go with it for now, but, you can redefine the system to have any type as the base type, meaning each corresponding dichotomy trait for that type is now the positive one.

What can it represent? Pretty much any system in socionics because everything was made with the same logic in mind. Specifically, the pyramid represent the abelian group Z2^4 (Z2 x Z2 x Z2 x Z2). But I don't like talking about the math because it is unnecessary and it tends to turn people off to the actual idea.

The image in the original post is a space showing all possible types, but a single type can be represented by defining the charge for each point (check out the post I just did for QuickTwist to see an example). For each type, all the small groups will have either 1 or 3 positive traits. They will look like the fano planes for the eight information elements and functions in the paper, except colored and 3d.

Thanks for the compliment, I put a lot of work into the visuals so it would make it easier for people to get into such an intense subject ^u^

Quote:

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Originally Posted by sindri

I think what you are asking is if there is a way to compare two types? Yes there is, here is a comparison of LII and LSI. This is the basics, let me know if you want to see more.

Bottom left are all eight dichotomies you must be to have introverted logic as your base. The other pyramids on the bottom center and left are the eight dichotomies that are different for each type. You are either all of one or the other. If you actually want to determine your type based on these, check out the 2003 reinin dichotomy study.
Attachment 7507

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OMG, thank you, this is brilliant!

OK so basically how this works is you take a commonality as the center and work off that, right?

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Originally Posted by Reficulris

I love it.
...
Making it an educational tool instead of a document would probably do two things:
1. make it much more likely to go viral (better marketing) 2. make it much more likely to get a longer exposure (play is easier then reading).

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Thanks so much! I tried really hard to make it understandable and I still am not sure if I succeed.

An interactive tool is the goal. My vision is to have an online celebrity typing tool that can analyze everyone's aggregate opinion and provide a framework for pinpoint debates. Also to develop a standardize methodology that could one day become a test. I've taken a C# and C++ programming class and for my final I made a working test with the error correction I described. If you know anyone who can help me make a website with users, a database as well as 3d graphics, I'm serious about making this thing. Send them my way please.

My short term goal is to finish this paper and then send it to DarkAngelFireWolf69 and Reinin, who both seem interested in this concept. If it is academic enough, I'd love to have it published in a journal.

Quote:

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Originally Posted by QuickTwist

OK so basically how this works is you take a commonality as the center and work off that, right?

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You could look at it like that.Since this is a system, you can isolate parts to focus on them, but remember, everything is happening at once and everything is dependent on everything else. This is every single socionics concept ever thought up in a single diagram. It is like a Rosetta stone because it shows how to translate one idea into another. Which specific part or property you want to use it up to you.

Quote:

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Originally Posted by sindri

Thanks so much! I tried really hard to make it understandable and I still am not sure if I succeed.

An interactive tool is the goal. My vision is to have an online celebrity typing tool that can analyze everyone's aggregate opinion and provide a framework for pinpoint debates. Also to develop a standardize methodology that could one day become a test. I've taken a C# and C++ programming class and for my final I made a working test with the error correction I described. If you know anyone who can help me make a website with users, a database as well as 3d graphics, I'm serious about making this thing. Send them my way please.

My short term goal is to finish this paper and then send it to DarkAngelFireWolf69 and Reinin, who both seem interested in this concept. If it is academic enough, I'd love to have it published in a journal.

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I don't think the concept is hard to understand, meaning knowing that everything affects something else, but it is difficult to see the detailed aspects of these differences. I don't know the dichotomies very well so I am just giving you the benefit of the doubt that you did it correctly. I can see where Mu is coming from as well. Its one of those things that if you take on faith that it works, it works, if you don't its going to take some time to understand. As I see it.

Quote:

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Originally Posted by QuickTwist

I don't think the concept is hard to understand, meaning knowing that everything affects something else, but it is difficult to see the detailed aspects of these differences. I don't know the dichotomies very well so I am just giving you the benefit of the doubt that you did it correctly. I can see where Mu is coming from as well. Its one of those things that if you take on faith that it works, it works, if you don't its going to take some time to understand. As I see it.

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This is my delima - I can either write a popular paper that is easy to understand but not very technical, or I can use mathimatical proofs to prove this not only works but it is a mathematical fact. I've been trying to write this damn thing for over a year, but I finally got closure when I talked to Reinin and DarkAngelFireWolf69 and they both said that they don't know the math, so I decided to write a popular paper and trust they will see the truth in it. I was thinking of including annotated proofs in the appendix, but it is a low priority now.

The basic flow of the proofs would be:
Prove the reinin dichotomies are abelian groups
Use the "fundamental theorem of abelian groups" to turn the abelian group into the internal direct product of Z2 cyclic groups
Show the order of this group is Z2^4
Show that is Isomorphic to the pyramid diagram
Use this property to project each trait onto the diagram to create a type of block design called a steiner system
Show the meaning of each subgroup

But see, even though I just proved everything to you, you still have to take my word for it, because you need to know some high level math to evaluate my contructions hahahaha. I'd rather not confuse people.

Quote:

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Originally Posted by sindri

This is my delima - I can either write a popular paper that is easy to understand but not very technical, or I can use mathimatical proofs to prove this not only works but it is a mathematical fact. I've been trying to write this damn thing for over a year, but I final got closure when I talked to Reinin and DarkAngelFireWolf69 and they both said that they don't know the math, so I decided to write a popular paper and trust they will see the truth in it. I was thinking of including annotated proofs in the appendix, but it is a low priority now.

They basic flow would be:
Prove the reinin dichotomies are abelian groups
Use the "fundamental theorem of abelian groups" to turn the abelian group into the internal direct product of Z2 cyclic groups
Show the order of this group is Z2^4
Show that is Isomorphic to the pyramid diagram
Use this property to project each trait onto the diagram to create a type of block design called a steiner system
Show the meaning of each subgroup

But see, even though I just proved everything to you, you still have to take my word for it hahahaha. I'd rather not confuse people.

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Do both, the universe needs stuff like this out there. I mean unless you really don't want to - I could understand that too, but by God it would be great knowing there was a proof about this out there somewhere.

@sindri, There is only one other person I know of (with my very limited knowledge) who came up with mathematical equation to prove human behavior and that was John Nash, and he ended up getting a Nobel Peace Prize. You are in good company.

Quote:

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Originally Posted by sindri

You are right, the ENTP notation is arbitrary, but it is the standard established by Reinin himself in his mathematics and is standard practice for all socionics. This is already complicated enough, so let's go with it for now, but, you can redefine the system to have any type as the base type, meaning each corresponding dichotomy trait for that type is now the positive one.

What can it represent? Pretty much any system in socionics because everything was made with the same logic in mind. Specifically, the pyramid represent the abelian group Z2^4 (Z2 x Z2 x Z2 x Z2). But I don't like talking about the math because it is unnecessary and it tends to turn people off to the actual idea.

The image in the original post is a space showing all possible types, but a single type can be represented by defining the charge for each point (check out the post I just did for QuickTwist to see an example). For each type, all the small groups will have either 1 or 3 positive traits. They will look like the fano planes for the eight information elements and functions in the paper, except colored and 3d.

Thanks for the compliment, I put a lot of work into the visuals so it would make it easier for people to get into such an intense subject ^u^

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Ok, cool, I wasn't criticizing with the ENTP being arbitrary btw, just wanted to understand the representation without any confusion on my part.

I have some more question and comments. I've always seen information preference typing as a matrix of traits(whatever) for which the solution is the type. This can apply to a empirical model as well not just socionics. Most big data marketing categorize people by some kind of single value decomposition which solves matrixs for any number of traits.
From what I understand a ableian group is just a special kind of matrix. This is essentially the same sort of technique you're proposing some sort of matrix solving technique.

There's a few directions this can be taken which can,

A. Guess at a type based on observed traits
B. Check type for accuracy
C. Derive additional traits

There's a few ways to do this.

Solve the Matrix to guess the type, then derive reinin from type and check this against traits

So Traits -> Type -> Reinin -> Parity check, I think this is close to your methodology?

This is pretty close to the way I see this occurring.

However, with enough data you can do something else too, which is find clusters of traits that arise in the data that we would need for the above method because you wouldn't really know what traits are applied to reinin.

So Traits -> Type -> Find traits clusters(should match Reinin)

The way I look at a socionics is that it presents a plausible solution to information precedence so this would be solution of some big data analysis where you would have type trait clusters and reinin trait clusters.

FWIW, you would not need to know what type these individual are or what even the data represents initially, you could do that by manually looking at the traits and associating with the sociotype.

Any big data analysis should produce some sort of type and sub clusters of dichotomies that matches Model A and Reinin Dichotomies. I think if a system can be created to analyze traits and create something that's close to socionics model(maybe not possible to be perfect because measurable traits are going to be likely behavior or self reporting) and then empirical out of this system can be analyzed for problems(which it will have) and inaccuracies.

I don't have a deep knowledge of the maths involved but you might so you might help me correct any understanding/misunderstanding I might have.

@mu4 i think you have the basic idea correct but the order is more flexible.

Once you have more than one dichotomy, you can begin to do a parity check. I see it as a dialectic process where the goal is to increase confidence and the problem becomes more complex as you go.

In my paper, all I did was solve for type and then fill in the remaining dichotomies to save space, but you can calculate each point one by one.

Basically these are the subgroups that I will get into later in the paper. I have a lot more to write about this topic.

# of independent dichotomies	# of dependent dichotomies in system that can be used for a parity check	total # of dichotomies in system, excluding the identity element (points)	total # of small groups in system (lines)	total # of dyad subspaces in system (surfaces)	number of possible types
1	0	1	0	0	8
2	1	3	1	0	4
3	4	7	7	1	2
4	11	15	35	15	1

Great stuff! I love this kind of mathematical analysis. I assume the 16th "null dichotomy" is need in order to match the power set of the original Jungian dichotomies. I'd love to see a more elegant way of describing it though.

Quote:

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Originally Posted by sindri

This is every single socionics concept ever thought up in a single diagram.

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I wouldn't quite go that far. For example, when it comes to kindred, look-alike, semi-duality and mirage relations, we don't classify them by traits but rather by functional equivalence in Model A.

Quote:

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Originally Posted by nefnaf

Great stuff! I love this kind of mathematical analysis.
...
I wouldn't quite go that far. For example, when it comes to kindred, look-alike, semi-duality and mirage relations, we don't classify them by traits but rather by functional equivalence in Model A.

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You don't know how happy it makes me to find a kindred spirit.

Even those relations can be represented with dichotomies if rationality is taken into account (the dichotomies that describe a rational kindred pair is the same the describe an irrational business pair, ect). The only thing off the top of my head that cannot be represented as dichotomies is information flow.

In general, I think that dichotomies are complementary to a model. Even if intertype relationships can be understood with dichotomies, the information element projection in model A is much more useful.

@sindri,

I have been debating my type and have some info on where I would classify myself.

From LII I am:

Intuitive
Democratic
Strategic
Farsighted
Judicious
Results
Asking


From LSI I am:

Declaring

For both I can't decide:

Positivist/Negativist

Gereral traits I share with both:

Introvert
Merry
Rational
Logical

General traits I am not:

Emotivest

So all the traits I have are:

Introvert
Intuitive
Logical
Rational

Static
Yielding
Democratic
Strategic
Constructivist
Farsighted

Merry
Judicious
Results

Declaring

And I cannot decide:

Positivist/Negativist


What would that make me?

Quote:

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Originally Posted by QuickTwist

So all the traits I have are:

Introvert	Static	Constructivist	Results
Intuitive	Yielding	Farsighted	Declaring
Logical	Democratic	Merry	Positivist / Negativist
Rational	Strategic	Judicious

What would that make me?

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Based on these dichotomies, you are most likely LII
Attachment 7511
Here are your relative dichotomies scores.

0	Introvert		+2	Static		-2	Constructivist		0	Results
+2	Intuitive		-2	Yielding		0	Farsighted		-4	Declaring
0	Logical		0	Democratic		0	Merry		+1	Negativist
0	Rational		+4	Strategic		+2	Judicious

The red represents the least harmonious. If you can prove they are wrong and changed them to their opposite, you will have 100% score of LII.

If you are certain you are have introverted logic as your base function, that resolves yielding and constructivist, leaving "declaring" as the only contradiction to LII.

My father is LII. One his sayings that demonstrates emotivism is "People rarely change their minds due to a good argument. You can prove them wrong but they will still not agree with you. The best way to change someone's mind is by being a friend." I personally would classify him as a declared because he does not like being interupted and he want enough time to make his point, but when he is teaching, he definitely uses the Socratic method. I've heard that asking/declaring isn't good for typing anyway. He definitely is obstinate, and my impression is the older he has gotten, the more time he has had to think out his own opinion and be certain of it. He's told me he wasn't like that when he was young. He is a negativist because he believes that any problems that are possible will happen. This may also be because he is a database administrator and given enough time, any error in computer code will happen. He is also very aware when a movie is presenting a philosophy he believes is false. Hope this gives you some ideas for yourself.

And of course, you could look up the following descriptions of functions and information elements. All the elements are hyperlinked, the number is the function
LII: 2Ne 4Se 6Si 8Ni
LSI 2Se 4Ne 6Ni 8Si

Oooooh here we go~~ Alot of these dichotomies really are shit, why? Well um how bout someone actually write about any of them?! :(


*****TEMPERAMENT X INTUITIVE/SENSING*****
//Bolded are the ones I think I am; Green means not enough info, Pink means I'm pretty sure :3 //
ISxp ~ Dynamic, Irrational, Introverted, Carefree, Judicious, Caregiver, Strategic!
INxp ~ Dynamic, irrational, Introverted, Farsighted, Decisive, Victim, Tactical!
INxj ~ Static, Rational, Introverted, Farsighted, Judicious, Infantile Strategic!
-------------------------------------------------------------------------------------- Not really considered if below this line
ENxp ~ Static, Rational, Extraverted, Carefree, Judicious, Infantile Tactical!
ISxj ~ Static, Rational, Introverted,Carefree, Decisive, Aggressor Tactical!
ESxj ~ Dynamic, Rational, Extraverted, Farsighted, Judicious, Caregiver Tactical!
ESxp ~ Static, irrational, Extraverted, Farsighted, Decisive, Aggressor Strategic!
ENxj ~ Dynamic, Rational, Extraverted, Carefree, Decisive, Victim, Tactical

AND SO.... INxj > ENxp > ISxj > ESxj > ENxj > INxp > ISxp = ESxp


~a message from me to this forum~

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AGHHHH I HATE THIS TEXT EDITOR, IT'S SPACING ALWAYS FUCKS UP EVERYTHING :( I HAD IT ALL LINED UP PERFECTLY, FUCK YOU...

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.... I might do more, especially since I hadn't touched Ethics or Logic yet. >_>

@Chryssie, I'm a bit confused by your post but I would be happy to analyze your results if you can put them in a way I understand.

Quote:

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Originally Posted by Chryssie

Well um how bout someone actually write about any of them?! :(

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The best Reinin dichotomy descriptions are the ones in the 2003 study [link]. Including the four Jungian dichotomies [link], there are a total of 15 dichotomies.

If you could rank you dichotomies in a single list like this, it will make it easy to calculate your results

Certainly: 100%-80% of the trait aspects fit you
Mostly: . .80% - 60% of the trait aspects fit you
Unsure: . .You are split between the two traits

For example, you could be certainly judicious, mostly intuitive and unsure of tactical/strategic. Feel free to throw in any small groups you're pretty certain of too but separate them from the dichotomies.

RIP Fresh Prince x_x

@sindri

Mmkay, thanks for your help I'd love to see my results whatever they may turn out to be :D

I put spoilers in just for unnecessary explanations on why I chose the dichotomy over the other, but it's not really something you need to read, it's just something to help me think through things. edit: forgive me, the text editor truly is a piece of crap -_-

[Dichotomies] Certain (80-100%)
Introversion

I never really knew how to measure this in myself, I do think my focus prefer to remain in my surroundings even if I'm very seemingly in my head. I get very easily lost though, it feels almost like I am dissociating from the world a lot from feeling overwhelmed by my physical/emotional/mental interactions with my surroundings.

I also don't have much initiative unless I'm in a situation that requires it.

Static

Unless I have this concept a bit warped in my head, I really do think I am a Static type according to the way my memory works and how I explain or describe things and events. I always see everything by its category, state, relationship with other people/objects, etc. and usually my stories are told in a very barebones way, like it's just a snapshot of what the event as whole felt like, with no added feelings or sensory details, usually just say it as it is. Also notable is my confusion of the Dynamic aspects of this world.. it's like it's turned off in my head or something, I'm really bad at following processes that take time where you have to focus on changes over states. I can't follow people's directions easily or remember how to get from one place to another, my memory in such areas are god awful. I really couldn't care less about how things will play out over time either, unless it is involving romantic fantasies. >w<

Constructivist

[Dichotomies] Very much relatable but still hesitant (70-80%)Strategic
Intuitive
Yielding

But all this means apparently is your level of motivation vs. the required "energy" to achieve something... I have no energy nor desires so I stay with what I have...

[Dichotomies] Less sure... (60-70%)
Positivism (I actually relate more to Positivism as described as one of DarkAngelFireWolf69's dichotomies for Cognitive Style, the "convergence of thinking". But this description by Reinin isn't as relatable.)
Aristocratic
Asking
Merry
Result

Honestly I can do both modes, but Result is more natural and satisfying tbh. I relate to process when it says it feels lost when it comes back to something in the middle of the process, this is very disorienting for me and it actually makes me want to start it all over again (in the case of video games, books, movies.. I just need to do everything in one sitting so I can get the whole feeling of it). But I am more oriented towards getting to the end tbh and tend to skip over much of the process so it doesn't become a pain in the butt.

[Dichotomies] Uncertain (50%)
Decisive

I think that I'm mostly hesitant about this because I'm not a very decisive person in the literal sense, in fact I don't do most of the things I consider doing on any given day, but if I do choose to actually go through with anything, it does feel like the decision is a part of who I am and whatever consequences happen are just of my own fault... even if it really isn't so, so I put alot of thought and energy into each decision, considering even the most irrelevant of factors, which is where my indecisiveness sets in. :p I do try to get everything done at once before considering relaxing at all, I feel guilty otherwise. I don't really "prepare" for anything, whether it involves relaxing my mind or body or spreading tasks over a period of time to make it easy on my energy reserves. I also dislike having others try and change my plans and decisions, it feels disrespectful and physically uncomfortable to switch over to another activity when I want to get what I'm doing, done now.

Rational
Ethical
Farsighted

@Chryssie I made an excel program to calculate your fuzzy logic, and I can conclude you are not asking or merry, making you decisively an EII

This is what the program output looks like. I'll put a link up top if anyone wants to play around with it.
Attachment 8665

Quote:

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Originally Posted by sindri

@Chryssie I made an excel program to calculate your fuzzy logic, and I can conclude you are not asking or merry, making you decisively an EII

This is what the program output looks like. I'll put a link up top if anyone wants to play around with it.
Attachment 8665

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Thank you so much, and yeah I didn't really feel like merry and asking were dichotomies very prominent in my personality, but they made sense upon reading the descriptions on wiki socion. I'm okay with ditching them though for Serious and Declaring. :D

So you think I'm process afterall? It's cool I turned out to be an ethical/rational/farsighted type even when they were said to be 50% correct xD

It's also good I finally have some evidence for being EII and not SEI/IEI/LII/SLI.

Pretty cool stuff, especially the visualising parts.

Quote:

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Originally Posted by Reficulris

What would be the next step from my perspective is to make a web-tool that allows you to flip the variables into their opposites dynamically so you can just "click" you way through the socion basically.

That would allow for a "ceteris paribus" approach of experimenting while keeping the overview intact :)\

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In the description, I've added an excel program that allows you to click on each dichotomy to select it. Thanks for the great idea. It took me a bit because I had to teach myself VBA to get it to work. Hopefully people will find this concept easier to understand with an interactive model.

Quote:

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Originally Posted by Pika Pika

Thank you so much, and yeah I didn't really feel like merry and asking were dichotomies very prominent in my personality, but they made sense upon reading the descriptions on wiki socion. I'm okay with ditching them though for Serious and Declaring. :D

So you think I'm process afterall? It's cool I turned out to be an ethical/rational/farsighted type even when they were said to be 50% correct xD

It's also good I finally have some evidence for being EII and not SEI/IEI/LII/SLI.

---

I noticed you changed your avatar to LII, not EII. These are the LII dichotomies, with a newly designed interface:

Attachment 9099

Awesome results: IEI 48%, 39% ESE and 30% LII.
Positive + traits :
Introvert
Farsighted
Posivitist
Merry
Result
The rest is controversial...

Attachment 9136


LII = LSI.

Pretty sure I'm an LII though. I did choose 3 dichotomies that conflicted with LII plus 2 undecided.

Quote:

---

Originally Posted by sindri

This is my delima - I can either write a popular paper that is easy to understand but not very technical, or I can use mathimatical proofs to prove this not only works but it is a mathematical fact. I've been trying to write this damn thing for over a year, but I finally got closure when I talked to Reinin and DarkAngelFireWolf69 and they both said that they don't know the math, so I decided to write a popular paper and trust they will see the truth in it. I was thinking of including annotated proofs in the appendix, but it is a low priority now.

The basic flow of the proofs would be:
Prove the reinin dichotomies are abelian groups
Use the "fundamental theorem of abelian groups" to turn the abelian group into the internal direct product of Z2 cyclic groups
Show the order of this group is Z2^4
Show that is Isomorphic to the pyramid diagram
Use this property to project each trait onto the diagram to create a type of block design called a steiner system
Show the meaning of each subgroup

---

Just in case you're still trying to do this:

Dichotomies form an abelian group under the XOR/interleaving operation (which has (A XOR B) and (A == B) as its two halves). It's pretty easy to show that this operation is commutative/abelian, and that X + X = 0 for all X. This immediately gives you that it's a product of Z2's. If you also define Reinin dichotomies as being generated by four independent dichotomies, then you get Z2^4.

That's just the math part though. I'm highly skeptical of typing people by tallying up Reinin dichotomies, to say the least.

Nothing in this thread to debate or assault. Sigh.

Quote:

---

Originally Posted by thehotelambush

Just in case you're still trying to do this:

Dichotomies form an abelian group under the XOR/interleaving operation (which has (A XOR B) and (A == B) as its two halves). It's pretty easy to show that this operation is commutative/abelian, and that X + X = 0 for all X. This immediately gives you that it's a product of Z2's. If you also define Reinin dichotomies as being generated by four independent dichotomies, then you get Z2^4

---

Yes, I am still interested. However, I would like to define each Z2 element as a sign group (the multiplicative group of +1 and -1) not with Boolean logic. It's been a while since I've written a proof. I think we know each other from the world socionics society. Are you interested in helping me or do you know of any good resources?

Quote:

---

Originally Posted by sindri

Yes, I am still interested. However, I would like to define each Z2 element as a sign group (the multiplicative group of +1 and -1) not with Boolean logic. It's been a while since I've written a proof. I think we know each other from the world socionics society. Are you interested in helping me or do you know of any good resources?

---

If you define it as a product of multiplication groups then it's basically abelian by definition and there is nothing to prove. The interesting part is that you can "multiply" the natural groupings of types (dichotomies) in such a way that they form a vector space.

Quote:

---

Originally Posted by thehotelambush

If you define it as a product of multiplication groups then it's basically abelian by definition and there is nothing to prove. The interesting part is that you can "multiply" the natural groupings of types (dichotomies) in such a way that they form a vector space.

---

If possible, I would like to write a long proof that does not take short cuts or apply laws only known to mathematicians to arrive at the answer. I'm assuming that almost everyone who reads this has not even heard of a graded vector spaces. Ideally, I would use only the most basic opperations and have a column next to each step explaining with words what I am doing and giving the appropiate background. If there is not a reasonable chance the layman could follow my proof, then it is not worth writing.

In school, I've been asked to recreate importaint proofs, like in physics and calculus. These proofs are facts, we know they work 100%, but the exercise shows "why" they work. I would like to include that "why" in all of my proofs.

Also, my final proof will be quite a bit more complex than just proving a single vectorspace or geometric projection. Eventually, I am going to take the direct product of multiple vector spaces. A great example is how the direct producted of the information elements and functions creates the 16 types or how the direct product of two types creates the intertype relations.

There is some nuance to this, as I think you have commented in your own article, because you can make the model appear unbalanced with out a full explanation. I think you define the supervisions rings as Dih4 if I remember right. This is unnecessary if you account for the rationality dichotomy, but i cannot just define the type dichotomies as z2 sign group and have that point understood.

@sindri 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?

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.

Quote:

---

There is some nuance to this, as I think you have commented in your own article, because you can make the model appear unbalanced with out a full explanation. I think you define the supervisions rings as Dih4 if I remember right. This is unnecessary if you account for the rationality dichotomy, but i cannot just define the type dichotomies as z2 sign group and have that point understood.

---

Maybe it's because abelian groups are easier to understand, or some fascination with Reinin dichotomies, but I am a bit puzzled why people want to somehow "prove" that the socion is actually abelian / a vector space (I've seen this attitude from Russians too). The relationship group is nonabelian no matter how you define it, because the mirror of my benefactor is not the benefactor of my mirror. The rings may derive from some underlying binary reality but the questions of why and how that occurs are still open. Until then, I am inclined to focus more on the relationships than the Reinin dichotomies.

Quote:

---

Originally Posted by thehotelambush

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.

Quote:

---

Originally Posted by thehotelambush

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.

Quote:

---

Originally Posted by thehotelambush

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.

I've created a list with all the small groups on wikisocion \(^u^)/. Now I'm working on adding something like this to the excel program.

http://www.wikisocion.org/en/index.php?title=Small_groups#Sortable_Small_Group_ Table

I had a Eureka moment and realized I could do the same analysis I've been doing with the small groups on the dyad and type level. I didn't want to have to figure out all of those equations, so I wrote a program to do it for me \(^u^)/

This is written in Python, which you can run in browser [link]. Otherwise, here is the code

#Harmony Calculation for dichotomy level reinin structures


#Cell Index for excel
#Input needs to be in a single column, in the order:
#E, N, T, P, EN, ET, EP, NT, NP, TP, ENT, ENP, ETP, NTP, ENTP


#Starting at cell F2 for dichotomy E
startColumn = 'F'
startRow = 2


#Assign variables to excel input cells, in vector numerical order
P= startColumn+str(startRow+ 3) #0001
T= startColumn+str(startRow+ 2) #0010
TP= startColumn+str(startRow+ 9) #0011
N= startColumn+str(startRow+ 1) #0100
NP= startColumn+str(startRow+ 8) #0101
NT= startColumn+str(startRow+ 7) #0110
NTP= startColumn+str(startRow+13) #0111
E= startColumn+str(startRow+ 0) #1000
EP= startColumn+str(startRow+ 6) #1001
ET= startColumn+str(startRow+ 5) #1010
ETP= startColumn+str(startRow+12) #1011
EN= startColumn+str(startRow+ 4) #1100
ENP= startColumn+str(startRow+11) #1101
ENT= startColumn+str(startRow+10) #1110
ENTP=startColumn+str(startRow+14) #1111


#Dichotomy vectors put in list in numerical order
cellList = ['IDENTITY',P,T,TP,N,NP,NT,NTP,E,EP,ET,ETP,EN,ENP,E NT,ENTP]


#Dichotomy variable from index number
nameList = ['IDENTITY','P','T','TP','N','NP','NT','NTP','E','E P','ET','ETP','EN','ENP','ENT','ENTP']


#List Index
list1= [''] #0000
listP= [''] #0001
listT= [''] #0010
listTP= [''] #0011
listN= [''] #0100
listNP= [''] #0101
listNT= [''] #0110
listNTP= [''] #0111
listE= [''] #1000
listEP= [''] #1001
listET= [''] #1010
listETP= [''] #1011
listEN= [''] #1100
listENP= [''] #1101
listENT= [''] #1110
listENTP= [''] #1111


listList =
[list1,listP,listT,listTP,listN,listNP,listNT,listN TP,listE,listEP,listET,listETP,listEN,listENP,list ENT,listENTP]


#FUNCTIONS
#Print list items with line space at end
def printList(arg1):

i = 0

loop=len(arg1)

while (i < loop):

print(arg1[i])

i = i + 1

print ("")

#Add new item to bottom of list
def addLast(item,list):

list.insert(len(list),item)

#vector addition for two dichotomy vectors strings
def vectorAdd (v1,v2):

v1=str(v1)

v2=str(v2)

a=( int(v1[0]) + int(v2[0]) )%2 #Mod 2 addition, 1+0=1 1+1=0

b=( int(v1[1]) + int(v2[1]) )%2

c=( int(v1[2]) + int(v2[2]) )%2

d=( int(v1[3]) + int(v2[3]) )%2

v3=str(a)+str(b)+str(c)+str(d) #Recontructs output vector string

return(v3)

#Converts boolean vector to decimal equivelent to use with list indexing
def vectorToInt (vector):

vector=str(vector)

a=int(vector[0])*8+int(vector[1])*4+int(vector[2])*2+int(vector[3])

return a

#Converts a number 0-15 into a vector string
def intToVector (integer):

integer = ''.join(str(1 & int(integer) >> i) for i in range(4)[::-1])

return integer

#Adds two integers as if they were vectors and returns an integer
def intAdd (int1, int2):

int1 = intToVector(int1)

int2 = intToVector(int2)

int3 = vectorAdd(int1,int2)

int3 = vectorToInt(int3)

return int3

#PROGRAM


#Small group level constructions, 7 for each dichotomy
w=1
while (w<16):

vw=intToVector(w) #w as a vector

x=w+1

while (x<16):

vx=intToVector(x) #x as a vector

if vw!=vx:

formula = '='+cellList[w]+'*'+cellList[x]

location = listList[vectorToInt(vectorAdd(vw,vx))]

addLast( formula, location)

x=x+1

w=w+1

#Dyad level constructions, 28 for each dichotomy
w=1
while (w<16):

vw=intToVector(w) #w as a vector

x=w+1

while (x<16):

vx=intToVector(x) #x as a vector

if w!=x:

y=x+1

while (y<16):

vy=intToVector(y) #y as a vector

if vectorAdd(vw,vx)!=vy:

formula = '='+cellList[w]+'*'+cellList[x]+'*'+cellList[y]

location = listList[vectorToInt(vectorAdd(vectorAdd(vw,vx),vy))]

addLast( formula, location)

y=y+1

x=x+1

w=w+1

#Type level constructions, 56 for each dichotomy
w=1
while (w<16):

vw=intToVector(w) #w as a vector

x=w+1

while (x<16):

vx=intToVector(x) #x as a vector

if w!=x:

y=x+1

while (y<16):

vy=intToVector(y) #y as a vector

if vectorAdd(vw,vx)!=vy and vw!=vy and vx!=vy:

z=y+1

while (z<16):

vv1=vw

vv2=vx

vv3=vy

vv4=vectorAdd(vw,vx)

vv5=vectorAdd(vw,vy)

vv6=vectorAdd(vx,vy)

vv7=vectorAdd(vectorAdd(vw,vx),vy)

vz=intToVector(z) #z as a vector

if (vz!=vv1) and (vz!=vv2) and (vz!=vv3) and (vz!=vv4) and (vz!=vv5) and (vz!=vv6) and (vz!=vv7):

formula = '='+cellList[w]+'*'+cellList[x]+'*'+cellList[y]+'*'+cellList[z]

location = listList[vectorToInt(vectorAdd(vectorAdd(vectorAdd(vw,vx),v y),vz))]

addLast( formula, location)

z=z+1

y=y+1

x=x+1

w=w+1

#PRINT RESULTS
#In vector numerical order, to be copied into Excel
i=1
while i<16:

vectorNum = i

print(nameList[vectorNum])

printList(listList[vectorNum])

print('--------------------')

print('')

i=i+1

#END PROGRAM

The program as posted is set to output excel cells for my dichotomy calculator. Changing a few things around [link], this is the output in Reinin notation:

E

Small Group Relations:
=N*EN
=T*ET
=P*EP
=NT*ENT
=NP*ENP
=TP*ETP
=NTP*ENTP


Dyad Relations:
=N*T*ENT
=N*P*ENP
=N*ET*NT
=N*EP*NP
=N*TP*ENTP
=N*ETP*NTP
=T*P*ETP
=T*EN*NT
=T*EP*TP
=T*NP*ENTP
=T*ENP*NTP
=P*EN*NP
=P*ET*TP
=P*NT*ENTP
=P*ENT*NTP
=EN*ET*ENT
=EN*EP*ENP
=EN*TP*NTP
=EN*ETP*ENTP
=ET*EP*ETP
=ET*NP*NTP
=ET*ENP*ENTP
=EP*NT*NTP
=EP*ENT*ENTP
=NT*NP*ETP
=NT*TP*ENP
=NP*TP*ENT
=ENT*ENP*ETP


Type Relations:
=N*T*P*ENTP
=N*T*EP*NTP
=N*T*NP*ETP
=N*T*TP*ENP
=N*P*ET*NTP
=N*P*NT*ETP
=N*P*TP*ENT
=N*ET*EP*ENTP
=N*ET*NP*TP
=N*ET*ENP*ETP
=N*EP*NT*TP
=N*EP*ENT*ETP
=N*NT*NP*ENTP
=N*NT*ENP*NTP
=N*NP*ENT*NTP
=N*ENT*ENP*ENTP
=T*P*EN*NTP
=T*P*NT*ENP
=T*P*NP*ENT
=T*EN*EP*ENTP
=T*EN*NP*TP
=T*EN*ENP*ETP
=T*EP*NT*NP
=T*EP*ENT*ENP
=T*NT*TP*ENTP
=T*NT*ETP*NTP
=T*TP*ENT*NTP
=T*ENT*ETP*ENTP
=P*EN*ET*ENTP
=P*EN*NT*TP
=P*EN*ENT*ETP
=P*ET*NT*NP
=P*ET*ENT*ENP
=P*NP*TP*ENTP
=P*NP*ETP*NTP
=P*TP*ENP*NTP
=P*ENP*ETP*ENTP
=EN*ET*EP*NTP
=EN*ET*NP*ETP
=EN*ET*TP*ENP
=EN*EP*NT*ETP
=EN*EP*TP*ENT
=EN*NT*NP*NTP
=EN*NT*ENP*ENTP
=EN*NP*ENT*ENTP
=EN*ENT*ENP*NTP
=ET*EP*NT*ENP
=ET*EP*NP*ENT
=ET*NT*TP*NTP
=ET*NT*ETP*ENTP
=ET*TP*ENT*ENTP
=ET*ENT*ETP*NTP
=EP*NP*TP*NTP
=EP*NP*ETP*ENTP
=EP*TP*ENP*ENTP
=EP*ENP*ETP*NTP

N

Small Group Relations:
=E*EN
=T*NT
=P*NP
=ET*ENT
=EP*ENP
=TP*NTP
=ETP*ENTP


Dyad Relations:
=E*T*ENT
=E*P*ENP
=E*ET*NT
=E*EP*NP
=E*TP*ENTP
=E*ETP*NTP
=T*P*NTP
=T*EN*ET
=T*EP*ENTP
=T*NP*TP
=T*ENP*ETP
=P*EN*EP
=P*ET*ENTP
=P*NT*TP
=P*ENT*ETP
=EN*NT*ENT
=EN*NP*ENP
=EN*TP*ETP
=EN*NTP*ENTP
=ET*EP*NTP
=ET*NP*ETP
=ET*TP*ENP
=EP*NT*ETP
=EP*TP*ENT
=NT*NP*NTP
=NT*ENP*ENTP
=NP*ENT*ENTP
=ENT*ENP*NTP


Type Relations:
=E*T*P*ENTP
=E*T*EP*NTP
=E*T*NP*ETP
=E*T*TP*ENP
=E*P*ET*NTP
=E*P*NT*ETP
=E*P*TP*ENT
=E*ET*EP*ENTP
=E*ET*NP*TP
=E*ET*ENP*ETP
=E*EP*NT*TP
=E*EP*ENT*ETP
=E*NT*NP*ENTP
=E*NT*ENP*NTP
=E*NP*ENT*NTP
=E*ENT*ENP*ENTP
=T*P*EN*ETP
=T*P*ET*ENP
=T*P*EP*ENT
=T*EN*EP*TP
=T*EN*NP*ENTP
=T*EN*ENP*NTP
=T*ET*EP*NP
=T*ET*TP*ENTP
=T*ET*ETP*NTP
=T*NP*ENT*ENP
=T*TP*ENT*ETP
=T*ENT*NTP*ENTP
=P*EN*ET*TP
=P*EN*NT*ENTP
=P*EN*ENT*NTP
=P*ET*EP*NT
=P*EP*TP*ENTP
=P*EP*ETP*NTP
=P*NT*ENT*ENP
=P*TP*ENP*ETP
=P*ENP*NTP*ENTP
=EN*ET*EP*ETP
=EN*ET*NP*NTP
=EN*ET*ENP*ENTP
=EN*EP*NT*NTP
=EN*EP*ENT*ENTP
=EN*NT*NP*ETP
=EN*NT*TP*ENP
=EN*NP*TP*ENT
=EN*ENT*ENP*ETP
=ET*NT*NP*ENP
=ET*NT*TP*ETP
=ET*NT*NTP*ENTP
=EP*NT*NP*ENT
=EP*NP*TP*ETP
=EP*NP*NTP*ENTP
=NT*TP*ENT*ENTP
=NT*ENT*ETP*NTP
=NP*TP*ENP*ENTP
=NP*ENP*ETP*NTP

T

Small Group Relations:
=E*ET
=N*NT
=P*TP
=EN*ENT
=EP*ETP
=NP*NTP
=ENP*ENTP


Dyad Relations:
=E*N*ENT
=E*P*ETP
=E*EN*NT
=E*EP*TP
=E*NP*ENTP
=E*ENP*NTP
=N*P*NTP
=N*EN*ET
=N*EP*ENTP
=N*NP*TP
=N*ENP*ETP
=P*EN*ENTP
=P*ET*EP
=P*NT*NP
=P*ENT*ENP
=EN*EP*NTP
=EN*NP*ETP
=EN*TP*ENP
=ET*NT*ENT
=ET*NP*ENP
=ET*TP*ETP
=ET*NTP*ENTP
=EP*NT*ENP
=EP*NP*ENT
=NT*TP*NTP
=NT*ETP*ENTP
=TP*ENT*ENTP
=ENT*ETP*NTP


Type Relations:
=E*N*P*ENTP
=E*N*EP*NTP
=E*N*NP*ETP
=E*N*TP*ENP
=E*P*EN*NTP
=E*P*NT*ENP
=E*P*NP*ENT
=E*EN*EP*ENTP
=E*EN*NP*TP
=E*EN*ENP*ETP
=E*EP*NT*NP
=E*EP*ENT*ENP
=E*NT*TP*ENTP
=E*NT*ETP*NTP
=E*TP*ENT*NTP
=E*ENT*ETP*ENTP
=N*P*EN*ETP
=N*P*ET*ENP
=N*P*EP*ENT
=N*EN*EP*TP
=N*EN*NP*ENTP
=N*EN*ENP*NTP
=N*ET*EP*NP
=N*ET*TP*ENTP
=N*ET*ETP*NTP
=N*NP*ENT*ENP
=N*TP*ENT*ETP
=N*ENT*NTP*ENTP
=P*EN*ET*NP
=P*EN*EP*NT
=P*ET*NT*ENTP
=P*ET*ENT*NTP
=P*EP*NP*ENTP
=P*EP*ENP*NTP
=P*NT*ENT*ETP
=P*NP*ENP*ETP
=P*ETP*NTP*ENTP
=EN*ET*EP*ENP
=EN*ET*TP*NTP
=EN*ET*ETP*ENTP
=EN*NT*NP*ENP
=EN*NT*TP*ETP
=EN*NT*NTP*ENTP
=ET*EP*NT*NTP
=ET*EP*ENT*ENTP
=ET*NT*NP*ETP
=ET*NT*TP*ENP
=ET*NP*TP*ENT
=ET*ENT*ENP*ETP
=EP*NT*TP*ENT
=EP*NP*TP*ENP
=EP*TP*NTP*ENTP
=NT*NP*ENT*ENTP
=NT*ENT*ENP*NTP
=NP*TP*ETP*ENTP
=TP*ENP*ETP*NTP

P

Small Group Relations:
=E*EP
=N*NP
=T*TP
=EN*ENP
=ET*ETP
=NT*NTP
=ENT*ENTP


Dyad Relations:
=E*N*ENP
=E*T*ETP
=E*EN*NP
=E*ET*TP
=E*NT*ENTP
=E*ENT*NTP
=N*T*NTP
=N*EN*EP
=N*ET*ENTP
=N*NT*TP
=N*ENT*ETP
=T*EN*ENTP
=T*ET*EP
=T*NT*NP
=T*ENT*ENP
=EN*ET*NTP
=EN*NT*ETP
=EN*TP*ENT
=ET*NT*ENP
=ET*NP*ENT
=EP*NT*ENT
=EP*NP*ENP
=EP*TP*ETP
=EP*NTP*ENTP
=NP*TP*NTP
=NP*ETP*ENTP
=TP*ENP*ENTP
=ENP*ETP*NTP


Type Relations:
=E*N*T*ENTP
=E*N*ET*NTP
=E*N*NT*ETP
=E*N*TP*ENT
=E*T*EN*NTP
=E*T*NT*ENP
=E*T*NP*ENT
=E*EN*ET*ENTP
=E*EN*NT*TP
=E*EN*ENT*ETP
=E*ET*NT*NP
=E*ET*ENT*ENP
=E*NP*TP*ENTP
=E*NP*ETP*NTP
=E*TP*ENP*NTP
=E*ENP*ETP*ENTP
=N*T*EN*ETP
=N*T*ET*ENP
=N*T*EP*ENT
=N*EN*ET*TP
=N*EN*NT*ENTP
=N*EN*ENT*NTP
=N*ET*EP*NT
=N*EP*TP*ENTP
=N*EP*ETP*NTP
=N*NT*ENT*ENP
=N*TP*ENP*ETP
=N*ENP*NTP*ENTP
=T*EN*ET*NP
=T*EN*EP*NT
=T*ET*NT*ENTP
=T*ET*ENT*NTP
=T*EP*NP*ENTP
=T*EP*ENP*NTP
=T*NT*ENT*ETP
=T*NP*ENP*ETP
=T*ETP*NTP*ENTP
=EN*ET*EP*ENT
=EN*EP*TP*NTP
=EN*EP*ETP*ENTP
=EN*NT*NP*ENT
=EN*NP*TP*ETP
=EN*NP*NTP*ENTP
=ET*EP*NP*NTP
=ET*EP*ENP*ENTP
=ET*NT*TP*ENT
=ET*NP*TP*ENP
=ET*TP*NTP*ENTP
=EP*NT*NP*ETP
=EP*NT*TP*ENP
=EP*NP*TP*ENT
=EP*ENT*ENP*ETP
=NT*NP*ENP*ENTP
=NT*TP*ETP*ENTP
=NP*ENT*ENP*NTP
=TP*ENT*ETP*NTP

EN

Small Group Relations:
=E*N
=T*ENT
=P*ENP
=ET*NT
=EP*NP
=TP*ENTP
=ETP*NTP


Dyad Relations:
=E*T*NT
=E*P*NP
=E*ET*ENT
=E*EP*ENP
=E*TP*NTP
=E*ETP*ENTP
=N*T*ET
=N*P*EP
=N*NT*ENT
=N*NP*ENP
=N*TP*ETP
=N*NTP*ENTP
=T*P*ENTP
=T*EP*NTP
=T*NP*ETP
=T*TP*ENP
=P*ET*NTP
=P*NT*ETP
=P*TP*ENT
=ET*EP*ENTP
=ET*NP*TP
=ET*ENP*ETP
=EP*NT*TP
=EP*ENT*ETP
=NT*NP*ENTP
=NT*ENP*NTP
=NP*ENT*NTP
=ENT*ENP*ENTP


Type Relations:
=E*T*P*NTP
=E*T*EP*ENTP
=E*T*NP*TP
=E*T*ENP*ETP
=E*P*ET*ENTP
=E*P*NT*TP
=E*P*ENT*ETP
=E*ET*EP*NTP
=E*ET*NP*ETP
=E*ET*TP*ENP
=E*EP*NT*ETP
=E*EP*TP*ENT
=E*NT*NP*NTP
=E*NT*ENP*ENTP
=E*NP*ENT*ENTP
=E*ENT*ENP*NTP
=N*T*P*ETP
=N*T*EP*TP
=N*T*NP*ENTP
=N*T*ENP*NTP
=N*P*ET*TP
=N*P*NT*ENTP
=N*P*ENT*NTP
=N*ET*EP*ETP
=N*ET*NP*NTP
=N*ET*ENP*ENTP
=N*EP*NT*NTP
=N*EP*ENT*ENTP
=N*NT*NP*ETP
=N*NT*TP*ENP
=N*NP*TP*ENT
=N*ENT*ENP*ETP
=T*P*ET*NP
=T*P*EP*NT
=T*ET*EP*ENP
=T*ET*TP*NTP
=T*ET*ETP*ENTP
=T*NT*NP*ENP
=T*NT*TP*ETP
=T*NT*NTP*ENTP
=P*ET*EP*ENT
=P*EP*TP*NTP
=P*EP*ETP*ENTP
=P*NT*NP*ENT
=P*NP*TP*ETP
=P*NP*NTP*ENTP
=ET*NP*ENT*ENP
=ET*TP*ENT*ETP
=ET*ENT*NTP*ENTP
=EP*NT*ENT*ENP
=EP*TP*ENP*ETP
=EP*ENP*NTP*ENTP
=NT*TP*ENT*NTP
=NT*ENT*ETP*ENTP
=NP*TP*ENP*NTP
=NP*ENP*ETP*ENTP

ET

Small Group Relations:
=E*T
=N*ENT
=P*ETP
=EN*NT
=EP*TP
=NP*ENTP
=ENP*NTP


Dyad Relations:
=E*N*NT
=E*P*TP
=E*EN*ENT
=E*EP*ETP
=E*NP*NTP
=E*ENP*ENTP
=N*T*EN
=N*P*ENTP
=N*EP*NTP
=N*NP*ETP
=N*TP*ENP
=T*P*EP
=T*NT*ENT
=T*NP*ENP
=T*TP*ETP
=T*NTP*ENTP
=P*EN*NTP
=P*NT*ENP
=P*NP*ENT
=EN*EP*ENTP
=EN*NP*TP
=EN*ENP*ETP
=EP*NT*NP
=EP*ENT*ENP
=NT*TP*ENTP
=NT*ETP*NTP
=TP*ENT*NTP
=ENT*ETP*ENTP


Type Relations:
=E*N*P*NTP
=E*N*EP*ENTP
=E*N*NP*TP
=E*N*ENP*ETP
=E*P*EN*ENTP
=E*P*NT*NP
=E*P*ENT*ENP
=E*EN*EP*NTP
=E*EN*NP*ETP
=E*EN*TP*ENP
=E*EP*NT*ENP
=E*EP*NP*ENT
=E*NT*TP*NTP
=E*NT*ETP*ENTP
=E*TP*ENT*ENTP
=E*ENT*ETP*NTP
=N*T*P*ENP
=N*T*EP*NP
=N*T*TP*ENTP
=N*T*ETP*NTP
=N*P*EN*TP
=N*P*EP*NT
=N*EN*EP*ETP
=N*EN*NP*NTP
=N*EN*ENP*ENTP
=N*NT*NP*ENP
=N*NT*TP*ETP
=N*NT*NTP*ENTP
=T*P*EN*NP
=T*P*NT*ENTP
=T*P*ENT*NTP
=T*EN*EP*ENP
=T*EN*TP*NTP
=T*EN*ETP*ENTP
=T*EP*NT*NTP
=T*EP*ENT*ENTP
=T*NT*NP*ETP
=T*NT*TP*ENP
=T*NP*TP*ENT
=T*ENT*ENP*ETP
=P*EN*EP*ENT
=P*EP*NP*NTP
=P*EP*ENP*ENTP
=P*NT*TP*ENT
=P*NP*TP*ENP
=P*TP*NTP*ENTP
=EN*NP*ENT*ENP
=EN*TP*ENT*ETP
=EN*ENT*NTP*ENTP
=EP*NT*ENT*ETP
=EP*NP*ENP*ETP
=EP*ETP*NTP*ENTP
=NT*NP*ENT*NTP
=NT*ENT*ENP*ENTP
=NP*TP*ETP*NTP
=TP*ENP*ETP*ENTP

EP

Small Group Relations:
=E*P
=N*ENP
=T*ETP
=EN*NP
=ET*TP
=NT*ENTP
=ENT*NTP


Dyad Relations:
=E*N*NP
=E*T*TP
=E*EN*ENP
=E*ET*ETP
=E*NT*NTP
=E*ENT*ENTP
=N*T*ENTP
=N*P*EN
=N*ET*NTP
=N*NT*ETP
=N*TP*ENT
=T*P*ET
=T*EN*NTP
=T*NT*ENP
=T*NP*ENT
=P*NT*ENT
=P*NP*ENP
=P*TP*ETP
=P*NTP*ENTP
=EN*ET*ENTP
=EN*NT*TP
=EN*ENT*ETP
=ET*NT*NP
=ET*ENT*ENP
=NP*TP*ENTP
=NP*ETP*NTP
=TP*ENP*NTP
=ENP*ETP*ENTP


Type Relations:
=E*N*T*NTP
=E*N*ET*ENTP
=E*N*NT*TP
=E*N*ENT*ETP
=E*T*EN*ENTP
=E*T*NT*NP
=E*T*ENT*ENP
=E*EN*ET*NTP
=E*EN*NT*ETP
=E*EN*TP*ENT
=E*ET*NT*ENP
=E*ET*NP*ENT
=E*NP*TP*NTP
=E*NP*ETP*ENTP
=E*TP*ENP*ENTP
=E*ENP*ETP*NTP
=N*T*P*ENT
=N*T*EN*TP
=N*T*ET*NP
=N*P*ET*NT
=N*P*TP*ENTP
=N*P*ETP*NTP
=N*EN*ET*ETP
=N*EN*NT*NTP
=N*EN*ENT*ENTP
=N*NT*NP*ENT
=N*NP*TP*ETP
=N*NP*NTP*ENTP
=T*P*EN*NT
=T*P*NP*ENTP
=T*P*ENP*NTP
=T*EN*ET*ENP
=T*ET*NT*NTP
=T*ET*ENT*ENTP
=T*NT*TP*ENT
=T*NP*TP*ENP
=T*TP*NTP*ENTP
=P*EN*ET*ENT
=P*EN*TP*NTP
=P*EN*ETP*ENTP
=P*ET*NP*NTP
=P*ET*ENP*ENTP
=P*NT*NP*ETP
=P*NT*TP*ENP
=P*NP*TP*ENT
=P*ENT*ENP*ETP
=EN*NT*ENT*ENP
=EN*TP*ENP*ETP
=EN*ENP*NTP*ENTP
=ET*NT*ENT*ETP
=ET*NP*ENP*ETP
=ET*ETP*NTP*ENTP
=NT*NP*ENP*NTP
=NT*TP*ETP*NTP
=NP*ENT*ENP*ENTP
=TP*ENT*ETP*ENTP

NT

Small Group Relations:
=E*ENT
=N*T
=P*NTP
=EN*ET
=EP*ENTP
=NP*TP
=ENP*ETP


Dyad Relations:
=E*N*ET
=E*T*EN
=E*P*ENTP
=E*EP*NTP
=E*NP*ETP
=E*TP*ENP
=N*P*TP
=N*EN*ENT
=N*EP*ETP
=N*NP*NTP
=N*ENP*ENTP
=T*P*NP
=T*ET*ENT
=T*EP*ENP
=T*TP*NTP
=T*ETP*ENTP
=P*EN*ETP
=P*ET*ENP
=P*EP*ENT
=EN*EP*TP
=EN*NP*ENTP
=EN*ENP*NTP
=ET*EP*NP
=ET*TP*ENTP
=ET*ETP*NTP
=NP*ENT*ENP
=TP*ENT*ETP
=ENT*NTP*ENTP


Type Relations:
=E*N*P*ETP
=E*N*EP*TP
=E*N*NP*ENTP
=E*N*ENP*NTP
=E*T*P*ENP
=E*T*EP*NP
=E*T*TP*ENTP
=E*T*ETP*NTP
=E*P*EN*TP
=E*P*ET*NP
=E*EN*EP*ETP
=E*EN*NP*NTP
=E*EN*ENP*ENTP
=E*ET*EP*ENP
=E*ET*TP*NTP
=E*ET*ETP*ENTP
=N*P*EN*ENTP
=N*P*ET*EP
=N*P*ENT*ENP
=N*EN*EP*NTP
=N*EN*NP*ETP
=N*EN*TP*ENP
=N*ET*NP*ENP
=N*ET*TP*ETP
=N*ET*NTP*ENTP
=N*EP*NP*ENT
=N*TP*ENT*ENTP
=N*ENT*ETP*NTP
=T*P*EN*EP
=T*P*ET*ENTP
=T*P*ENT*ETP
=T*EN*NP*ENP
=T*EN*TP*ETP
=T*EN*NTP*ENTP
=T*ET*EP*NTP
=T*ET*NP*ETP
=T*ET*TP*ENP
=T*EP*TP*ENT
=T*NP*ENT*ENTP
=T*ENT*ENP*NTP
=P*EN*NP*ENT
=P*ET*TP*ENT
=P*EP*NP*ETP
=P*EP*TP*ENP
=P*NP*ENP*ENTP
=P*TP*ETP*ENTP
=EN*EP*ENT*ENP
=EN*TP*ENT*NTP
=EN*ENT*ETP*ENTP
=ET*EP*ENT*ETP
=ET*NP*ENT*NTP
=ET*ENT*ENP*ENTP
=EP*NP*ENP*NTP
=EP*TP*ETP*NTP
=NP*ETP*NTP*ENTP
=TP*ENP*NTP*ENTP

NP

Small Group Relations:
=E*ENP
=N*P
=T*NTP
=EN*EP
=ET*ENTP
=NT*TP
=ENT*ETP


Dyad Relations:
=E*N*EP
=E*T*ENTP
=E*P*EN
=E*ET*NTP
=E*NT*ETP
=E*TP*ENT
=N*T*TP
=N*EN*ENP
=N*ET*ETP
=N*NT*NTP
=N*ENT*ENTP
=T*P*NT
=T*EN*ETP
=T*ET*ENP
=T*EP*ENT
=P*ET*ENT
=P*EP*ENP
=P*TP*NTP
=P*ETP*ENTP
=EN*ET*TP
=EN*NT*ENTP
=EN*ENT*NTP
=ET*EP*NT
=EP*TP*ENTP
=EP*ETP*NTP
=NT*ENT*ENP
=TP*ENP*ETP
=ENP*NTP*ENTP


Type Relations:
=E*N*T*ETP
=E*N*ET*TP
=E*N*NT*ENTP
=E*N*ENT*NTP
=E*T*P*ENT
=E*T*EN*TP
=E*T*EP*NT
=E*P*ET*NT
=E*P*TP*ENTP
=E*P*ETP*NTP
=E*EN*ET*ETP
=E*EN*NT*NTP
=E*EN*ENT*ENTP
=E*ET*EP*ENT
=E*EP*TP*NTP
=E*EP*ETP*ENTP
=N*T*EN*ENTP
=N*T*ET*EP
=N*T*ENT*ENP
=N*EN*ET*NTP
=N*EN*NT*ETP
=N*EN*TP*ENT
=N*ET*NT*ENP
=N*EP*NT*ENT
=N*EP*TP*ETP
=N*EP*NTP*ENTP
=N*TP*ENP*ENTP
=N*ENP*ETP*NTP
=T*P*EN*ET
=T*P*EP*ENTP
=T*P*ENP*ETP
=T*EN*NT*ENP
=T*ET*NT*ETP
=T*ET*TP*ENT
=T*EP*TP*ENP
=T*NT*ENT*ENTP
=T*TP*ETP*ENTP
=P*EN*NT*ENT
=P*EN*TP*ETP
=P*EN*NTP*ENTP
=P*ET*EP*NTP
=P*ET*TP*ENP
=P*EP*NT*ETP
=P*EP*TP*ENT
=P*NT*ENP*ENTP
=P*ENT*ENP*NTP
=EN*ET*ENT*ENP
=EN*TP*ENP*NTP
=EN*ENP*ETP*ENTP
=ET*EP*ENP*ETP
=ET*NT*ENT*NTP
=ET*TP*ETP*NTP
=EP*NT*ENP*NTP
=EP*ENT*ENP*ENTP
=NT*ETP*NTP*ENTP
=TP*ENT*NTP*ENTP

TP

Small Group Relations:
=E*ETP
=N*NTP
=T*P
=EN*ENTP
=ET*EP
=NT*NP
=ENT*ENP


Dyad Relations:
=E*N*ENTP
=E*T*EP
=E*P*ET
=E*EN*NTP
=E*NT*ENP
=E*NP*ENT
=N*T*NP
=N*P*NT
=N*EN*ETP
=N*ET*ENP
=N*EP*ENT
=T*EN*ENP
=T*ET*ETP
=T*NT*NTP
=T*ENT*ENTP
=P*EN*ENT
=P*EP*ETP
=P*NP*NTP
=P*ENP*ENTP
=EN*ET*NP
=EN*EP*NT
=ET*NT*ENTP
=ET*ENT*NTP
=EP*NP*ENTP
=EP*ENP*NTP
=NT*ENT*ETP
=NP*ENP*ETP
=ETP*NTP*ENTP


Type Relations:
=E*N*T*ENP
=E*N*P*ENT
=E*N*ET*NP
=E*N*EP*NT
=E*T*EN*NP
=E*T*NT*ENTP
=E*T*ENT*NTP
=E*P*EN*NT
=E*P*NP*ENTP
=E*P*ENP*NTP
=E*EN*ET*ENP
=E*EN*EP*ENT
=E*ET*NT*NTP
=E*ET*ENT*ENTP
=E*EP*NP*NTP
=E*EP*ENP*ENTP
=N*T*EN*EP
=N*T*ET*ENTP
=N*T*ENT*ETP
=N*P*EN*ET
=N*P*EP*ENTP
=N*P*ENP*ETP
=N*EN*NT*ENP
=N*EN*NP*ENT
=N*ET*NT*ETP
=N*EP*NP*ETP
=N*NT*ENT*ENTP
=N*NP*ENP*ENTP
=T*EN*ET*NTP
=T*EN*NT*ETP
=T*ET*NT*ENP
=T*ET*NP*ENT
=T*EP*NT*ENT
=T*EP*NP*ENP
=T*EP*NTP*ENTP
=T*NP*ETP*ENTP
=T*ENP*ETP*NTP
=P*EN*EP*NTP
=P*EN*NP*ETP
=P*ET*NT*ENT
=P*ET*NP*ENP
=P*ET*NTP*ENTP
=P*EP*NT*ENP
=P*EP*NP*ENT
=P*NT*ETP*ENTP
=P*ENT*ETP*NTP
=EN*ET*ENT*ETP
=EN*EP*ENP*ETP
=EN*NT*ENT*NTP
=EN*NP*ENP*NTP
=ET*NP*ETP*NTP
=ET*ENP*ETP*ENTP
=EP*NT*ETP*NTP
=EP*ENT*ETP*ENTP
=NT*ENP*NTP*ENTP
=NP*ENT*NTP*ENTP

ENT

Small Group Relations:
=E*NT
=N*ET
=T*EN
=P*ENTP
=EP*NTP
=NP*ETP
=TP*ENP


Dyad Relations:
=E*N*T
=E*P*NTP
=E*EN*ET
=E*EP*ENTP
=E*NP*TP
=E*ENP*ETP
=N*P*ETP
=N*EN*NT
=N*EP*TP
=N*NP*ENTP
=N*ENP*NTP
=T*P*ENP
=T*ET*NT
=T*EP*NP
=T*TP*ENTP
=T*ETP*NTP
=P*EN*TP
=P*ET*NP
=P*EP*NT
=EN*EP*ETP
=EN*NP*NTP
=EN*ENP*ENTP
=ET*EP*ENP
=ET*TP*NTP
=ET*ETP*ENTP
=NT*NP*ENP
=NT*TP*ETP
=NT*NTP*ENTP


Type Relations:
=E*N*P*TP
=E*N*EP*ETP
=E*N*NP*NTP
=E*N*ENP*ENTP
=E*T*P*NP
=E*T*EP*ENP
=E*T*TP*NTP
=E*T*ETP*ENTP
=E*P*EN*ETP
=E*P*ET*ENP
=E*EN*EP*TP
=E*EN*NP*ENTP
=E*EN*ENP*NTP
=E*ET*EP*NP
=E*ET*TP*ENTP
=E*ET*ETP*NTP
=N*T*P*EP
=N*T*NP*ENP
=N*T*TP*ETP
=N*T*NTP*ENTP
=N*P*EN*NTP
=N*P*NT*ENP
=N*EN*EP*ENTP
=N*EN*NP*TP
=N*EN*ENP*ETP
=N*EP*NT*NP
=N*NT*TP*ENTP
=N*NT*ETP*NTP
=T*P*ET*NTP
=T*P*NT*ETP
=T*ET*EP*ENTP
=T*ET*NP*TP
=T*ET*ENP*ETP
=T*EP*NT*TP
=T*NT*NP*ENTP
=T*NT*ENP*NTP
=P*EN*ET*EP
=P*EN*NT*NP
=P*ET*NT*TP
=P*EP*NP*TP
=P*EP*ENP*ETP
=P*NP*ENP*NTP
=P*TP*ETP*NTP
=EN*ET*NP*ENP
=EN*ET*TP*ETP
=EN*ET*NTP*ENTP
=EN*EP*NT*ENP
=EN*NT*TP*NTP
=EN*NT*ETP*ENTP
=ET*EP*NT*ETP
=ET*NT*NP*NTP
=ET*NT*ENP*ENTP
=EP*NP*ENP*ENTP
=EP*TP*ETP*ENTP
=NP*TP*NTP*ENTP
=ENP*ETP*NTP*ENTP

ENP

Small Group Relations:
=E*NP
=N*EP
=T*ENTP
=P*EN
=ET*NTP
=NT*ETP
=TP*ENT


Dyad Relations:
=E*N*P
=E*T*NTP
=E*EN*EP
=E*ET*ENTP
=E*NT*TP
=E*ENT*ETP
=N*T*ETP
=N*EN*NP
=N*ET*TP
=N*NT*ENTP
=N*ENT*NTP
=T*P*ENT
=T*EN*TP
=T*ET*NP
=T*EP*NT
=P*ET*NT
=P*EP*NP
=P*TP*ENTP
=P*ETP*NTP
=EN*ET*ETP
=EN*NT*NTP
=EN*ENT*ENTP
=ET*EP*ENT
=EP*TP*NTP
=EP*ETP*ENTP
=NT*NP*ENT
=NP*TP*ETP
=NP*NTP*ENTP


Type Relations:
=E*N*T*TP
=E*N*ET*ETP
=E*N*NT*NTP
=E*N*ENT*ENTP
=E*T*P*NT
=E*T*EN*ETP
=E*T*EP*ENT
=E*P*ET*ENT
=E*P*TP*NTP
=E*P*ETP*ENTP
=E*EN*ET*TP
=E*EN*NT*ENTP
=E*EN*ENT*NTP
=E*ET*EP*NT
=E*EP*TP*ENTP
=E*EP*ETP*NTP
=N*T*P*ET
=N*T*EN*NTP
=N*T*NP*ENT
=N*P*NT*ENT
=N*P*TP*ETP
=N*P*NTP*ENTP
=N*EN*ET*ENTP
=N*EN*NT*TP
=N*EN*ENT*ETP
=N*ET*NT*NP
=N*NP*TP*ENTP
=N*NP*ETP*NTP
=T*P*EP*NTP
=T*P*NP*ETP
=T*EN*ET*EP
=T*EN*NT*NP
=T*ET*NT*TP
=T*ET*ENT*ETP
=T*EP*NP*TP
=T*NT*ENT*NTP
=T*TP*ETP*NTP
=P*ET*EP*ENTP
=P*ET*NP*TP
=P*EP*NT*TP
=P*EP*ENT*ETP
=P*NT*NP*ENTP
=P*NP*ENT*NTP
=EN*ET*NP*ENT
=EN*EP*NT*ENT
=EN*EP*TP*ETP
=EN*EP*NTP*ENTP
=EN*NP*TP*NTP
=EN*NP*ETP*ENTP
=ET*EP*NP*ETP
=ET*NT*ENT*ENTP
=ET*TP*ETP*ENTP
=EP*NT*NP*NTP
=EP*NP*ENT*ENTP
=NT*TP*NTP*ENTP
=ENT*ETP*NTP*ENTP

ETP

Small Group Relations:
=E*TP
=N*ENTP
=T*EP
=P*ET
=EN*NTP
=NT*ENP
=NP*ENT


Dyad Relations:
=E*N*NTP
=E*T*P
=E*EN*ENTP
=E*ET*EP
=E*NT*NP
=E*ENT*ENP
=N*T*ENP
=N*P*ENT
=N*EN*TP
=N*ET*NP
=N*EP*NT
=T*EN*NP
=T*ET*TP
=T*NT*ENTP
=T*ENT*NTP
=P*EN*NT
=P*EP*TP
=P*NP*ENTP
=P*ENP*NTP
=EN*ET*ENP
=EN*EP*ENT
=ET*NT*NTP
=ET*ENT*ENTP
=EP*NP*NTP
=EP*ENP*ENTP
=NT*TP*ENT
=NP*TP*ENP
=TP*NTP*ENTP


Type Relations:
=E*N*T*NP
=E*N*P*NT
=E*N*ET*ENP
=E*N*EP*ENT
=E*T*EN*ENP
=E*T*NT*NTP
=E*T*ENT*ENTP
=E*P*EN*ENT
=E*P*NP*NTP
=E*P*ENP*ENTP
=E*EN*ET*NP
=E*EN*EP*NT
=E*ET*NT*ENTP
=E*ET*ENT*NTP
=E*EP*NP*ENTP
=E*EP*ENP*NTP
=N*T*P*EN
=N*T*ET*NTP
=N*T*TP*ENT
=N*P*EP*NTP
=N*P*TP*ENP
=N*EN*ET*EP
=N*EN*NT*NP
=N*EN*ENT*ENP
=N*ET*NT*TP
=N*EP*NP*TP
=N*NT*ENT*NTP
=N*NP*ENP*NTP
=T*P*NT*ENT
=T*P*NP*ENP
=T*P*NTP*ENTP
=T*EN*ET*ENTP
=T*EN*NT*TP
=T*ET*NT*NP
=T*ET*ENT*ENP
=T*NP*TP*ENTP
=T*TP*ENP*NTP
=P*EN*EP*ENTP
=P*EN*NP*TP
=P*EP*NT*NP
=P*EP*ENT*ENP
=P*NT*TP*ENTP
=P*TP*ENT*NTP
=EN*ET*TP*ENT
=EN*EP*TP*ENP
=EN*NT*ENT*ENTP
=EN*NP*ENP*ENTP
=ET*EP*NT*ENT
=ET*EP*NP*ENP
=ET*EP*NTP*ENTP
=ET*NP*TP*NTP
=ET*TP*ENP*ENTP
=EP*NT*TP*NTP
=EP*TP*ENT*ENTP
=NT*NP*NTP*ENTP
=ENT*ENP*NTP*ENTP

NTP

Small Group Relations:
=E*ENTP
=N*TP
=T*NP
=P*NT
=EN*ETP
=ET*ENP
=EP*ENT


Dyad Relations:
=E*N*ETP
=E*T*ENP
=E*P*ENT
=E*EN*TP
=E*ET*NP
=E*EP*NT
=N*T*P
=N*EN*ENTP
=N*ET*EP
=N*NT*NP
=N*ENT*ENP
=T*EN*EP
=T*ET*ENTP
=T*NT*TP
=T*ENT*ETP
=P*EN*ET
=P*EP*ENTP
=P*NP*TP
=P*ENP*ETP
=EN*NT*ENP
=EN*NP*ENT
=ET*NT*ETP
=ET*TP*ENT
=EP*NP*ETP
=EP*TP*ENP
=NT*ENT*ENTP
=NP*ENP*ENTP
=TP*ETP*ENTP


Type Relations:
=E*N*T*EP
=E*N*P*ET
=E*N*NT*ENP
=E*N*NP*ENT
=E*T*P*EN
=E*T*NT*ETP
=E*T*TP*ENT
=E*P*NP*ETP
=E*P*TP*ENP
=E*EN*ET*EP
=E*EN*NT*NP
=E*EN*ENT*ENP
=E*ET*NT*TP
=E*ET*ENT*ETP
=E*EP*NP*TP
=E*EP*ENP*ETP
=N*T*EN*ENP
=N*T*ET*ETP
=N*T*ENT*ENTP
=N*P*EN*ENT
=N*P*EP*ETP
=N*P*ENP*ENTP
=N*EN*ET*NP
=N*EN*EP*NT
=N*ET*NT*ENTP
=N*EP*NP*ENTP
=N*NT*ENT*ETP
=N*NP*ENP*ETP
=T*P*ET*ENT
=T*P*EP*ENP
=T*P*ETP*ENTP
=T*EN*ET*TP
=T*EN*NT*ENTP
=T*ET*EP*NT
=T*EP*TP*ENTP
=T*NT*ENT*ENP
=T*TP*ENP*ETP
=P*EN*EP*TP
=P*EN*NP*ENTP
=P*ET*EP*NP
=P*ET*TP*ENTP
=P*NP*ENT*ENP
=P*TP*ENT*ETP
=EN*ET*ENT*ENTP
=EN*EP*ENP*ENTP
=EN*NT*TP*ENT
=EN*NP*TP*ENP
=ET*EP*ETP*ENTP
=ET*NT*NP*ENT
=ET*NP*TP*ETP
=EP*NT*NP*ENP
=EP*NT*TP*ETP
=NT*NP*ETP*ENTP
=NT*TP*ENP*ENTP
=NP*TP*ENT*ENTP
=ENT*ENP*ETP*ENTP

ENTP

Small Group Relations:
=E*NTP
=N*ETP
=T*ENP
=P*ENT
=EN*TP
=ET*NP
=EP*NT


Dyad Relations:
=E*N*TP
=E*T*NP
=E*P*NT
=E*EN*ETP
=E*ET*ENP
=E*EP*ENT
=N*T*EP
=N*P*ET
=N*EN*NTP
=N*NT*ENP
=N*NP*ENT
=T*P*EN
=T*ET*NTP
=T*NT*ETP
=T*TP*ENT
=P*EP*NTP
=P*NP*ETP
=P*TP*ENP
=EN*ET*EP
=EN*NT*NP
=EN*ENT*ENP
=ET*NT*TP
=ET*ENT*ETP
=EP*NP*TP
=EP*ENP*ETP
=NT*ENT*NTP
=NP*ENP*NTP
=TP*ETP*NTP


Type Relations:
=E*N*T*P
=E*N*ET*EP
=E*N*NT*NP
=E*N*ENT*ENP
=E*T*EN*EP
=E*T*NT*TP
=E*T*ENT*ETP
=E*P*EN*ET
=E*P*NP*TP
=E*P*ENP*ETP
=E*EN*NT*ENP
=E*EN*NP*ENT
=E*ET*NT*ETP
=E*ET*TP*ENT
=E*EP*NP*ETP
=E*EP*TP*ENP
=N*T*EN*NP
=N*T*ET*TP
=N*T*ENT*NTP
=N*P*EN*NT
=N*P*EP*TP
=N*P*ENP*NTP
=N*EN*ET*ENP
=N*EN*EP*ENT
=N*ET*NT*NTP
=N*EP*NP*NTP
=N*NT*TP*ENT
=N*NP*TP*ENP
=T*P*ET*NT
=T*P*EP*NP
=T*P*ETP*NTP
=T*EN*ET*ETP
=T*EN*NT*NTP
=T*ET*EP*ENT
=T*EP*TP*NTP
=T*NT*NP*ENT
=T*NP*TP*ETP
=P*EN*EP*ETP
=P*EN*NP*NTP
=P*ET*EP*ENP
=P*ET*TP*NTP
=P*NT*NP*ENP
=P*NT*TP*ETP
=EN*ET*ENT*NTP
=EN*EP*ENP*NTP
=EN*NT*ENT*ETP
=EN*NP*ENP*ETP
=ET*EP*ETP*NTP
=ET*NT*ENT*ENP
=ET*TP*ENP*ETP
=EP*NP*ENT*ENP
=EP*TP*ENT*ETP
=NT*NP*ETP*NTP
=NT*TP*ENP*NTP
=NP*TP*ENT*NTP
=ENT*ENP*ETP*NTP

Now I just have to figure out how to factor in information metabolism and the higher order objects, like small groups, dyads and types. I might also want to put things in both positive and negative terms, like someone who is an introvert necessarily is not and extrovert.

Right
Click
​..+
Loop

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https://www.youtube.com/watch?v=Q7GSbcqw5P8

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Thanks so much for creating these diagrams and all the information. I am using this extensively! Can you please tell what is the name program you used for creating the pyramid which are on youtube videos? Thanks in advance!

Quote:

---

Originally Posted by Elstner

Thanks so much for creating these diagrams and all the information. I am using this extensively! Can you please tell what is the name program you used for creating the pyramid which are on youtube videos? Thanks in advance!

---

Thanks! I put in all the work just for people like you <3

I used 3DS MAX for the modeling and rendering (series of individual .png images), and VEGAS 14 for compiling the image sequences into 60fps HD video. If you have a student email, you have access to all autodesk products, but if you've never used a 3d modeling program, 3DS MAX has a steep learning curve. Adobe After Effects is the industry standard program for post processing, I'm just using VEGAS 14 because I got it for $20 in a humble bundle.

...Unless you're also talking about the graphics in the article and excel program lol, I made those with the shape tools in word and excel ;.D

I ran 20,000 random trials through my dichotomy analyzer algorithm and got this very narrow distribution curve. The harmony score, which measures how well the inputed traits theoretically agree with each other, can range from -35 to +91. In most science, 5% error is the gold standard for research, which translates to any score between +2.2 to +91. If I rate myself with the reinin dichotomies, I get a score of +35, which is well outside the random range.


I look forward to eventually putting together a test and applying this algorithm to see how the actual scores differ from purely random scores. If it is well outside the random range, it is empirical proof that the test, and by extension socionics, works.

Full Range (bin size .5):
Attachment 12989

Zoomed on peak (bin size is .1):
Attachment 12983

It will be significant

How's your harmony score calculated? I find it strange that the random data clumped up so tightly around 0.

Quote:

---

Originally Posted by ouronis

How's your harmony score calculated? I find it strange that the random data clumped up so tightly around 0.

---

This curve was generated by randomly selecting all 15 dichotomy traits on a 5 likert scale (an even chance of –1, –.5, 0, +.5, +1), and recording the results 20,000 times.

Since then, I've run 100,000 cycles with an 11 likert model, and included the output in the new version of the excel file [link]. If you open it, remember to download, open in excel and enable editing and content. On the "Input" tab are all the options, and you can click the random button to see how it works. I've added comments that will tell you about the buttons if you hover your mouse over them. You can also run your own experiment on the 6th "Random Experiment" tab, just start low to see how your computer handles then number crunching.

All the equations are on the "(Harmony Calc)" tab, if you want to figure out how it works.

This is the result of how I rate myself. You can see even though there is variation, there are clear column stripes. If you put in a random result, the field will look like tv static.

11

Ever since @thehotelambush showed be there are additional dichotomies (we've been calling Tencer dichotomies), I've been trying to wrap my head around them. I just had a break through when I built a program to combine the Reinin and Tencer dichotomies, and it turns out they only generate 8 additional dichotomies! I'm in shock, that is so much more manageable than what I was expecting

https://repl.it/@ajsindri/Group-Generator

The new dichotomy space is the 8 yellow tables. All spaces share the black dichotomies in common.

looks like tetris

After an existential crisis, I've decide to redo all my 4x4 tables to show Jung's type compass cycle. These are the changes:




In this new convention, here are all 32 structural type dichotomies.



I'll start updating all of my programs, article, charts, videos, ect, but I'm in the middle of a college semester, so it might be a while. The old tables still work great, but the new ones should be easier to see patterns with.

did you know strat has her own extension of reinin dichotomies? its interesting she has words for all the new combinations and works them into her narrative too. I like "smoothies" which is one of them

Quote:

---

Originally Posted by Bertrand

did you know strat has her own extension of reinin dichotomies? its interesting she has words for all the new combinations and works them into her narrative too. I like "smoothies" which is one of them

---

Naw, I don't really care about the definitions. I'm trying to work out the math so everyone can come to the table and figure out what details work and which don't. There are so many different ideas and theories, that level of synthesis is beyond the ability of a person, but we can do it as a community with the right structure.

This is some more exploratory work trying to reconcile the Reinin and Tencer interpretations and trying to see if a Dihedral Four Group can be generated from the compass dichotomies. I know these are complicated, but the whole point is try to integrate as much information together as possible to see if there is an underlying shape that makes sense of the whole pattern. Instructions are in the 3rd image. Feel free to ask questions if you feel lost.

This is a matrix for every combination of orbital, Reinin, Tencer and cross dichotomies. The color cells are + and the white cells are - . You can view with google, but if you download and open in Excel, the first row and column are always displayed, which is almost an essential feature if you want to reference this table. Also, the top right of each matrix is commented with the dichotomy traits.

https://drive.google.com/open?id=1vYppKMzPHpR7MTJGzrnGi4AP1yTnr-w3

This is how the harmony value could be used to test socionic theory.