Reinin dichotomies

From Wikisocion

Reinin dichotomies (also Reinin traits) are a set of 15 type dichotomies that divide the socion into symmetrical halves. Grigoriy Reinin (St. Petersburg, Russia), a mathematician and psychologist and one of the earliest socionists, mathematically proved the existence of these dichotomies, and their approximate content was elaborated by Aushra Augusta. Her work, The Theory of Reinin's Traits, published in 1985, was intended to be an introduction to the 15 dichotomies — a draft of sorts — but further definitive works have not yet been written on the subject. The usefulness of many or most Reinin dichotomies is consistently questioned by many socionists. Some use all of them in diagnosis, some use just a few more obvious ones (depending on the socionist's personal observations), and some do not use them at all.

The first four dichotomies correspond to the "Jungian foundation," or the four original Jungian dichotomies.

In common use the term "Reinin dichotomies" often refers only to the 11 non-Jungian dichotomies.

Reinin dichotomies
Carefree and farsighted	Yielding and obstinate	Static and dynamic
Democratic and aristocratic	Tactical and strategic	Constructivist and emotivist
Positivist and negativist	Judicious and decisive	Merry and serious
Process and result		Asking and declaring

1 Mathematics
2 Complete list
3 Reinin dichotomies as combinations
4 Empirical aspects
5 Comparison with Model A
6 Criticism
7 Possible dichotomous explanations
8 See also
9 Links

[edit] Mathematics

Dichotomies can be represented as elements of the four-dimensional vector space V = F₂⁴, where F₂ is the field containing only two elements, 1 and 0. For example, 1000 could represent the extroversion and introversion dichotomy. One basis for this vector space is in fact the Jungian basis, where the nth dichotomy just has a 1 in the nth position (this is called the "standard basis"). What this means is, each dichotomy can be expressed as a unique linear combination of the Jungian dichotomies. In this setting, a linear combination just amounts to a sum. But what is a sum of dichotomies?

We add dichotomies by adding them bit-wise, with the convention that 1 + 1 = 0. Given this convention a+b=c implies b+c=a and c+a=b. E.g., static = E + P = 1000 + 0001 = 1001. We can also think of this operation as bit-wise exclusive or: each resulting digit is a 1 if and only if exactly one of the input digits is.

If a set of vectors contains a vector that can be written as the sum of some other vectors in the set, we call the vectors dependent. Otherwise, they are independent. By basic linear algebra, a basis is exactly a maximal independent set.

Given an arbitrary choice for which type the 0 vector represents, the set of types can be identified with the same vector space. We choose ENTp = 0000. Thus, e.g., ISFj = 1111 and ISTp = 1100. We can put the two vector spaces together to get something interesting: the dot product, defined by (a,b,c,d).(a',b',c',d') = aa' + bb' + cc' + dd', is a way to determine which types satisfy which traits. Whether dichotomy . type is 0 or 1 tells us which pole the type is on, 0 being "same as ENTp" (since ENTp always gives 0). E.g., positivist . ISTp = 1110 . 1100 = 1*1 + 1*1 = 0. Hence, ISTp is indeed a positivist, same as ENTp. All the dot product means is: add up all the basic traits that questioner is dependent on, counting E, N, T, P as 0 and the opposites as 1. Thus, each significant 1 corresponds to a "flip".

Each basis of the vector space of dichotomies represents a different choice of four basic dichotomies. The dot product is an example of a more general kind of vector operation, called a symmetric bilinear form, which satisfies

Symmetry: v.w = w.v
Linearity: (av + v').w = a(v.w) + v'.w

Here a is a scalar, either 0 or 1. Given a symmetric bilinear form and a special kind of basis, one can determine what the coefficients of v will be in terms of this basis. The basis {e_i} must be orthonormal, meaning e_i.e_j = 1 if i=j and 0 otherwise. Given an orthonormal basis, the coefficient v has on e_i is just v.e_i.

The standard basis is obviously orthonormal in terms of the dot product. What other orthonormal bases are there? The dot product of v and w just gives the parity (even or odd) of the number of positions in which v and w both have 1s. So for a vector to give 1 when dotted with itself, it must have an odd number of 1s. In dimension four, this only allows 1 or 3 1s in each vector. Let's call these types "1" or "3" for short.

Four "1"s is just the standard basis, since no two vectors can be the same. Otherwise: no "3" can overlap with any "1", so we cannot have more than 1 "1", but in fact we can't even have 1 "1", because then the only vectors must be, e.g., 1110 and 0001, which do not form a basis.

Therefore the only remaining possibility is all "3"s. There are only (4 choose 3) = (4 choose 1) = 4 distinct such vectors, so they must be just the 2's complement of (that is, 1111 -) the standard basis. This is in fact a second orthonormal basis, and the only other. In any vector space over F₂, the complement of an orthonormal basis is orthonormal if and only if the dimension of the vector space, n, is even.

Proof: The "only if" part is obvious, since odd - odd = even. Let U be the vector consisting of all 1s. Then for v and w in an orthonormal basis we have (U-v).(U-w) = U.U - U.w - U.v + v.w. U.U = 0 because n is even. U.w just counts the number of 1s in w, and same for v. Since v and w both have an odd number of ones, U.w - U.v must be even, and hence is 0. Therefore (U-v).(U-w) = v.w.

So the dot product tells us nothing about what coefficients vectors will have in most bases - not much of a surprise, since it is defined in terms of the standard basis. (In vector spaces over "continuous" fields such as the real numbers, there is more flexibility.)

[edit] Complete list

Given four basic dichotomies, one can form 11 new ones dependent on the basic four. That is, when constructing the Reinin dichotomies, each of the original dichotomies (or places in the 4-letter code) has two possible coefficients, 1 or 0 — either it will be included or it will not. This produces 2^4 = 16 options.

The first of these, where no letter or Jungian dichotomy will be included, is not a dichotomy proper, as it does not split the socion. (This is just another way of saying that 0 cannot be a basis vector.) The remaining 15 are the type dichotomies.

(Note that the base type for denoting the dichotomies is arbitrary, but ENTP is the standard for historical reasons.)

(null/nonnull)
E (extroversion/introversion)
N (intuitive/sensing)
T (logical/ethical)
P (irrational/rational)
EN (carefree/farsighted)
ET (obstinate/compliant) (also 'yielding/obstinacy' or 'resource-protecting/ interest-protecting')
EP (static/dynamic)
NT (democratic/aristocratic)
NP (tactical/strategic)
TP (constructivist/emotivist)
ENT (positivist/negativist)
ENP (reasonable/resolute) (also 'judicious/decisive')
ETP (merry/serious) (also 'subjectivist/objectivist')
NTP (process/result)(also called 'left/right' and 'evolutory/involutory')
ENTP (questioning/declaring) (also 'asking/declaring' or 'interrogative/declarative')

The "two-letter" Reinin dichotomies are called two-tier, and so on. The one-letter dichotomies are just the original Jungian dichotomies, though they are equally covered by the Reinin model.

[edit] Reinin dichotomies as combinations

From the above proof, we see that the Reinin dichotomies can be thought of as combinations of the original four.

C = n!/(k!(n-k)!)

Where k is the number of elements in the subset and n is the number of elements in the set that is drawn from.

Here there are 4 elements in the original set (E-I, N-S, T-F and P-J). The new sets will have between 2 to 4 parameters, so the number of Reinin dichotomies (not including the original four) is:

4!/(2!(4-2)!) + 4!/(3!(4-3)!) + 4!/(4!(4-4)!) = 6 + 4 + 1 = 11

It's also easy to find out the combinations on pen and paper. Simply find all the ways you can combine four predefined letters (or any other things) into groups of two, three and four, where the order doesn't matter.

[edit] Empirical aspects

Above the Reinin dichotomies are mathematically defined. Whether they have empirical content, on the other hand, is a completely separate matter. Whether the content is well-defined at all is one of the main criticisms of Reinin dichotomies.

The content of several of the derived dichotomies comes naturally from other standard parts of socionics theory. But as the correspondence between the dichotomy and Model A becomes more complex, so does the dichotomy's content become less obvious based on purely theoretical considerations.

Some of the simpler correspondences between the functional and dichotomous models:

Intuitive/sensing and logic/ethics determine a type's strengths and weaknesses;
Introversion/extroversion coincides with the orientation of the leading function (as well as all contact functions);
Rationality/irrationality similarly coincides with the "rhythm" of the accepting functions;
Static/dynamic determines the conscious (or "mental") elements in a type's formula;
Aristocratic/democratic determines which elements are blocked together;
Reasonable/resolute and subjectivist/objectivist correspond to quadra values;

An interesting question is, can Reinin dichotomies be considered equal in their significance to the original Jungian dichotomies? After all, the derivation works in reverse too. Only speculation can provide an answer at this point. A humorous counterexample is the dichotomies of gender and blood type (reference). Obviously the conjunction of the two via * is totally meaningless. That said, the fact that Reinin dichotomies' content can be elaborated at all is a testament to the highly general nature of socionic type, whose component dichotomies combine to form an integrated whole, represented mathematically as the nonnull trait: the human being.

[edit] Comparison with Model A

The central idea of socionics is that types are unbalanced entities. This understanding is built into Model A, but not into Reinin dichotomies. Therefore, Reinin dichotomies must be supplemented with other theoretical apparatus in order to explain things like relationships as fully as Model A. This could be a good thing in that Reinin dichotomies show the theoretical possibility of isolating the assumptions implicit in Model A and showing which are independent of which.

A few socionists, such as Mironov and others from St. Petersburg, consider the Reinin dichotomies to actually be information processing mechanisms. Three such dichotomy traits combine to form an information element. Most socionists consider the Reinin dichotomies to be divisions whose meaning can only be understood by analyzing their effect on Model A.

[edit] Criticism

It might be said that the Reinin traits should be treated dichotomously instead of, or at least in addition to, in terms of information elements and Model A. The fundamental difference between rational and irrational information elements is not built into the Reinin model. Also, it has no concept of element dominance (i.e. functional ordering). It doesn't necessarily render the tools used in Model A useless, but it should be stressed that the classical traits have a purely dichotomous definition, so they should also be explainable using only dichotomies. In fact it is likely that any regular categorization system will also be reflected in Model A in some more or less regular way—this observation doesn't prove anything however.

[edit] Possible dichotomous explanations

The most natural way to discover the meaning of the dichotomies is as a conflict or harmonizing of some sort between pairs of traits. For example, rationals want stability, but dynamics perceive change, creating a tendency for EJs to want to actively influence their environment to control that change - extroversion. Likewise, irrationals are more comfortable with fluid change, but statics see things as staying the same - which leads them to actively create the change in their environment (also extroversion).

An interesting area of research here would be interclub or intertemperament relationships. We would also need to establish descriptions for the other multiple-dichotomical categories, such as E/I combined with S/N, and so on.