The Mathematical Basis of Reinin Dichotomies

[Exodus]

Reinin dichotomies were derived using group theory, a field of math I know very little about. This site gives a thorough explanation. Unfortunately it is in Russian, and online translators obviously don't do very well with the mathematical terminology. That said, maybe misutii and any resident mathematicians could help out.

I'll try to explain my current understanding of it as simply as possible. The idea is that the socion, with its dichotomies, is a Klein 4-group. This means, given a few initial dichotomies, you can produce all other possible symmetric dichotomies. (I'm not sure what symmetric means in this context.)

New dichotomies can be formed by combining the original four dichotomies. If I, N, T, and J are represented by 1 (true) and their opposites by 0 (false), comparing them with the boolean operation of equivalence (=) yields new dichotomies. For instance, a type is "static" if I and J are both true or both false. Mathematically, I=J. (The above article uses the clumsy but equivalent notation (I & J) v (~I & ~J) instead.) Any other commutative (i.e. symmetric) operation, such as XOR, could also be used.

4C2 = 6 dichotomies are formed by comparing pairs of the original four dichotomies.

farsighted: I=N
obstinate: I=T
static: I=J
democratic: N=T
strategic: N=J
emotivist: T=J

(Note that the resulting names are all applicable to INTj, because of the way we chose our truth values at the beginning. Unfortunately there are no neutral names for each dichotomy; one is forced to say Static-Dynamic. However, it's easy to do this based on any other type.)

These new second-order dichotomies can be compared to create even more dichotomies.

For example,

reasonable: static=N : (I=J)=N
subjectivist: static=T : (I=J)=T

However, the number of distinct combinations is limited by the properties of equivalence. (I=J)=T is the same as (T=I)=J, because equivalence is associative--that is to say, the order doesn't matter--as well as commutative. Given that, you might as well just get rid of the equals signs and parentheses, and write the original dichotomies that each new dichotomy depends on.

Including the original dichotomies, for completeness:

I: I
N: N
T: T
J: J
farsighted: IN
obstinate: IT
static: IJ
democratic: NT
strategic: NJ
emotivist: TJ
negativist: INT
reasonable: INJ
merry: ITJ
result: NTJ
questioner: INTJ

There is but a single fourth-order dichotomy: Questioner-Declarer. I have heard that Aushra identified this one herself. Coincidence?

Except for the first- and second-order dichotomies, it is a bit difficult to use these definitions in practice. Scroll to the bottom to see a more useful list, adapted from anndelise's summary.

My result shows a constraint on what kind of dichotomies are allowed: it must either always switch when one of the original dichotomies is switched, or be completely independent of that dichotomy. For example, changing J/P always changes Static-Dynamic, but changing N/S never does.

Since a dichotomy can depend on 1, 2, 3, or 4 of the original dichotomies,

all in all we have

4C1 + 4C2 + 4C3 + 4C4 = 15 dichotomies.

Remember Pascal's Triangle? sum(nCr over r=0...n) = 2[sup:52435fcc25]n[/sup:52435fcc25]. Therefore, since we exclude the null dichotomy (which isn't really a dichotomy at all) there must be 2[sup:52435fcc25]4[/sup:52435fcc25] - 1 dichotomies in all; 4 original and 11 Reinin. I suppose there is also a group-theoretical explanation for this. An interesting consequence is that in any dichotomy-based type theory the total number of dichotomies is 1 less than the number of types!

I mentioned before that every pair of non-identical types shares exactly 7 dichotomies. Why 7? (This is another question for our imaginary mathematician.)

Since Reinin dichotomies treat the socion symmetrically, there is a slight mismatch between functional and dichotomal interpretations. For instance, in asymmetrical relations, sometimes one's Supervisor shares the Reasonable dichotomy, and sometimes not. However, all the symmetrical relationships are consistent in this respect. When I can, I will post a table showing the dichotomy changes for each relationship. I think the ones for Duality, Conflict, and the other intra-quadra relations may be especially revealing.

farsighted = IN + ES
careless/happy-go-lucky = EN + IS

obstinate = IT + EF
compliant = ET + IF

static = Ij + Ep
dynamic = Ip + Ej

democratism = Q1 + Q3 = NT + SF
aristocrats = Q2 + Q4 = ST + NF

tactical = Np + Sj
strategic = Sp + Nj

constructivist = Fj + Tp
emotivist = Tj + Fp

process/rightist = PQ1 + JQ2 + PQ3 + JQ4 = NTp + SFp + STj + NFj
result/leftist = JQ1 + PQ2 + JQ3 + PQ4 = NTj + SFj + STp + NFp

cheerful/gay/subjectivism: Q1 + Q2 = ITj + EFj + IFp + ETp
serious/objectivist: Q3 + Q4 = ITp + EFp + IFj + ETj

reasonable = Q1 + Q4 = INj + ESj + ISp + ENp
resolute/decisive = Q2 + Q3 = INp + ESp + ISj + ENj

positivist = EQ1 + IQ2 + EQ3 + IQ4 = ENT + ESF + IST + INF
negativist = IQ1 + EQ2 + IQ3 + EQ4 = INT + ISF + EST + ENF

asker/taciturn = NQ1 + NQ2 + SQ3 + SQ4 = TQ1 + FQ2 + FQ3 + TQ4
declarer/narrative = SQ1 + SQ2 + NQ3 + NQ4 = FQ1 + TQ2 + TQ3 + FQ4

[machintruc]

oldforumlinkviewtopic.php?t=9020

[Exodus]

Thanks for the reference. I didn't realize the extent of Smilingeyes's writings on the dichotomies. Cool stuff.

[Jonathan]

Thanks...I was trying to remember the name of this. Years ago I was trying to relate to MBTI to group theory and was trying to remember the names of some stuff in this post http://the16types.info/forums/viewto...ighlight=group.

As Smilex pointed out to to me, any group of four types may be seen as symmetrical, depending on which base dichotomies one uses.

Without question, the idea of the Reinin dichotomies is very powerful. What I have always been skeptical about, however, is the descriptions. How do we know that the descriptions are accurate? Unlike the calculation of how many dichotomies one can come up with, etc., the descriptions of behavior for each dichotomy isn't derived mathematically, as far as I know. Rather, it's based either on observations on some people, or on a person's theoretical conception on what that dichotomy should be like, or both.

Recently, I was questioning the reasonable/resolute dichotomy. The description of reasonable sounded so much like Ip behavior, and that for resolute sounded so much like Ej behavior, that I questioned if they're really valid. Expat suggested that one should apply the Reinin dichotomies only after having settled the more basic dichotomies. But that leaves open the question of whether the descriptions for each are correct or helpful.

[Exodus]

Yeah, I was more interested in the math behind it, which as far as I know has not yet been fully described anywhere but on the page I mentioned.

[krieger]

Does anyone know why Augusta & co. say these dichotomies resulted from a 'wrong hypothesis'?

Did they ever explicitly state what is wrong with them?

[Joy]

The Mathematical Basis of Reinin Dichotomies

I think the mathematical structure of the dichotomies is more of a result than a cause.

[Jonathan]

Does anyone know why Augusta & co. say these dichotomies resulted from a 'wrong hypothesis'?

Did they ever explicitly state what is wrong with them?

This is interesting to me; where did you hear Augusta/etc say that? I've often mentioned my own assessment that there are different schools within Socionists; this would be a confirmation.

Although I don't know what was said about them, I do know some possible problems and reasons why they may to conflict with Augusta's approach. As I've mentioned, certain dichotomy descriptions may be confounded with rat/irrat or other distinctions, and thus appear to conflict with the common Socionicis view of what each type is like.

But the main problem occurs if a person starts to think of each dichotomy as equally important.

It seems the core of Augusta's research had to do with understanding why certain groups of people seem to get along more easily than others (at least in long-term relationships, etc.). This of course has to do with the concept of functions being in the same I/E orientation. It can be shown, however, that if one views all the possible dichotomies as equal, then one could synthetically produce alternative functions that, while having the same structure as the original model, would contradict Socionics hypotheses on what types do best together.

[meatburger]

oldforumlinkviewtopic.php?t=9020

HOLY SHIT

[Rick]

Does anyone know why Augusta & co. say these dichotomies resulted from a 'wrong hypothesis'?

Did they ever explicitly state what is wrong with them?

I think Dmitri Lytov says this, but I don't know about Augusta. She talks about some of them in her books.

[Expat]

Expat suggested that one should apply the Reinin dichotomies only after having settled the more basic dichotomies. But that leaves open the question of whether the descriptions for each are correct or helpful.

I don't remember having quite suggested that -- but it doesn't matter. I agree with this:

Unlike the calculation of how many dichotomies one can come up with, etc., the descriptions of behavior for each dichotomy isn't derived mathematically, as far as I know. Rather, it's based either on observations on some people, or on a person's theoretical conception on what that dichotomy should be like, or both.

The only way dichotomies or other groupings of human behavior can be useful is if they are validated by observations of real people. I have found that, if understood, and applied carefully, dichotomies indeed "move together" as expected. However, it's a big mistake to use them, individually, in a black-and-white way, to rule out types - as in, "she's not an asker, so I will rule out all the asker types in her case" etc.

Personally, if I'm observing someone IRL, I hardly ever actually use the dichotomies to type them - other traits, such as temperament and quadras, become visible first.

[Exodus]

The Mathematical Basis of Reinin Dichotomies

I think the mathematical structure of the dichotomies is more of a result than a cause.

Huh? The thread title refers to how they are derived from the basic structure of the socion.

[misutii]

Reinin dichotomies were derived using group theory, a field of math I know very little about. This site gives a thorough explanation. Unfortunately it is in Russian, and online translators obviously don't do very well with the mathematical terminology. That said, maybe misutii and any resident mathematicians could help out.

lol i'm flattered but using my name in the same paragraph as one that uses the term "math" that many times is probably a federal offense... just warning you now in case the FBI comes knocking down your door this week with bazookas and the swat team taking aim from the building across the street as riots break out due to the genocide of neanderthals by our hands and 15,000 years of repressed human rage over the common question "what is the meaning of life?"

anyways I'll take a look at the page later when this damn exam is over -_-

[Exodus]

lol, thanks.

So little time...

[CuriousSoul]

I would love to see these Reinin dichotomies tied to practical observations more closely.
They seem to make a lot of sense, but is it just in my head?

The only way dichotomies or other groupings of human behavior can be useful is if they are validated by observations of real people. I have found that, if understood, and applied carefully, dichotomies indeed "move together" as expected. However, it's a big mistake to use them, individually, in a black-and-white way, to rule out types - as in, "she's not an asker, so I will rule out all the asker types in her case" etc.

Very true.

[krieger]

This group-theoretical explanation of the dichotomies is interesting, but still a bit sketchy. Does it follow from the mathematics which reinin attributes connect which concrete and abstract attributes? Was the concreteness/abstractness of functions, and with those the arrangement of functions in a cycle derived from the math, or were these founded on an independant observation?

[Exodus]

It's funny to read this now that I actually understand group theory. Here is an updated version:

https://drive.google.com/file/d/0Bxs...ew?usp=sharing