Dichotomies formulas

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Метасоционика

Classification of Reinin dichotomies.
Formulas and generations

Reinin-Model A relation (Rei-mA)
The following set of diagrams and formulas is an attempt to describe Socions symmetries. Considering Model A a mapping of Information Elements(IMEs) to Functions(Fns), Reinin dichotomies would form special invariants in this mapping. Each Reinin dichotomy can be written as a formula expressing the symmetry in the set of IMEs mapping to symmetry in the set of Fns. Usually it looks like “these elements” are gonna be in “these functions”, and it everything is expressed in informational and functional dichotomies

The classic example of it is Static/Dynamic if you are static then static elements are present in you mental ring, as formula it would be a mapping of [static IME] → (mental Fns). This is the simplest example of such invariant formulas, they get more and more complex. Actually such formulas and mapping are kinda like building bricks of Model A as a permutation, as a mapping of 8 IMEs to 8 Fns.

The complexity and formula varies from dichotomy to dichotomy. There are several classifications and explanations of Reinin-model A connection. The most well known Western classification is made by Andrew Joyton and described by the following diagram

Semyon Churiumov’s discovery of Hadamard matrix as socionics structure, postulating strict order on every level of IM and the structure of each level he preceded the Generations of dichotomies theory in socionics, which helps to understand principles of rei-mA connection.

There are 322 560 different possibilities to place TIMs on Hadamard matrix which lead to different TIM-Reinin correspondences, but only the one Churiumov suggested shows very interesting properties:

Each level has its own complete meaning and scale of generality
The first 3 levels semantically correspond to Churiumov’s axioms
There is a legacy property to dichotomies which appears on different levels
the legacy and the formula of rei-mA invariant are related to a specific place in system which is all explained by Generations theory

Generations theory connects each dichotomy to the level of Information Metabolism it appears on. Each level there are new dichotomies appearing and the old dichotomies inheriting their fractal (scale-invariant) place.

here’s the complete list of DIchotomies with the fractal diagram showing their generation:

The generations inherit the place in system where they were first originated. The 1st generation holds 1st 2 places. The 2nd generation holds the last 2 places. The 3rd generation hold 2 before and 2 after the equator. The 4th generation takes in-between place.

Depending on generations there are 3 classes of Reinins related to rei-mA invariant:

ancient dichotomies 1 and 2 generations:
vertness (extravert/introvert)
nality (irrational/rational)
tality (static/dynamic)

have (4→4)x2 mapping formula

3 generation dichotomies:
carefree/farsighted
intuitive/sensory
yielding/obstinate
logic/Ethic
merry/Serious
constructivist/Emotivist
judicious/decisive
tactical/strategic

have (2→4)x2 formula mapping IMEs of only one nality (ir or ra)

4 generation dichotomies:

democrat/aristocrat
+/- (positivist/negativist)
process/result
?/! (asking/declaring)

the 4gen dichotomies connect generation theory with plexus theory. 4gen dichotomies link elements of different nality in model A showing a completely new way of looking at symmetries. they don’t say where exactly IME is gonna be, they show the combinations of IMEs, how they are placed related to each other. 4 gen dichotomies have the most complex formulas sometimes even requiring Gulenko-Newman set of informational/functional dichotomies

The formulas of the most gen4 dichotomies (except process/result) are expressed as eqiuvalences: democrat/aristocrat is classical example
in horizontal blocking democrats have Intuition + Logic or Sensorics + Ethics, that might be expressed at a mapping of elements equivalent by Detached /involved dichotomy are mapped to the horizontal (Freudian) blockings, read more in democrat/aristocrat section

+/- and ?/! are expressed in Gulenko-Newman Dichotomies. The formulas of these 2 dichotomies requires another coordinate system to be expressed, read more in +/- section.

4 generation dichotomies have (~2→~2) formula of equivalence
its uses 4 tetrachotomies for demo/ari
2 tetrachotomies for +/- and ?/!
1 tetrachotomy for proc/res

Extravert/Introvert (Vertness)

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

The first dichotomy belongs to Generation 1. The fractal position is next to the first “existence” (valid/null) dichotomy. Generated by Vertness of level3 [extraverted/introverted IME] and (bold/cautious Fn). Hence these 2 dichotomies participate in Vertness invariant formula

Extravert/Introvert mapping formula:

—Extravert—
[Ne Fe Te Se | Extraverted] → (1 3 6 8 | Bold)
[Si Ti Fi Ni | Introverted] → (2 4 5 7 | Cautious)

—Introvert—
[Si Ti Fi Ni| Introverted] → (1 3 6 8 | Bold)
[Ne Fe Te Se | Extraverted] → (2 4 5 7 | Cautious)

Ne	Si	Fe	Ti
Te	Fi	Se	Ni

→

1	2
4	3
6	5
7	8

Being in ancient dichotomy class Vert has (4→4)x2 formula type, distributes 4 IMEs (extra) into 4 functions (Bold) and does it twice - hence x2-: being a counterpart intro IMEs are mapped to cautious FNs due to model A entanglement, so all the 8 elements are mapped. That’s an important property.

carefree/farsighted

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

Generation 3
The first dichotomy of the 3rd generation, which has another type of formula: (2→4)x2
gen3 dichotomies distribute 2 couples of equal nality IMEs, so the other nality IMEs are left uncertain. carefree/farsighted distributes pairs of dual irrational elements to evaluatory/situational functions. To formulize such a mapping we would need not only informational dichotomies but their multiplication - informational tetrachotomies - the 2 specific that form dual IMEs and faculties. These 2 IME tetrachotomies is enough to formulate all the 8 gen3 dichotomies, that’s the way gen3 informational dichotomies entangle and form gen3 reinins.

to form these 2 IME couples we’ll need to multiply delta/beta and alpha/gamma, which give Nality as a result. this is dyadic dichotomy, which means dual TIMs have this dichotomy in the same polarity. Qadric and dyadic dichotomies correspond to extravert TIMs and distribute dual pairs of IMEs.

“judicious” dichotomies (the ones corresponding to judicious TIMs) distribute irrational elements, because the dont inherit the place near the equator, where the rational IMEs are distributed

Carefree
[Ne Si | delta, alpha, irrational] → (1 4 5 8 | evaluatory)
[Ni Se | beta, gamma, irrational] → (2 3 6 7 | situational)

Farsighted
[Ni Se | beta, gamma, irrational] → (1 4 5 8 | evaluatory)
[Ne Si | delta, alpha, irrational] → (2 3 6 7 | situational)

Ne	Si
		Se	Ni

intuitive/sensory

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

Being the first individual - which duals have different - intutive/sensory distributes another IME couples, the pairs of opposite vertness elements

Distributes Intuition/Sensorics Faculty to strong/weak functions, leaves rational IMEs uncertain.

intuitive formula
[Ne Ni | Detached implicit irrational] → (1 2 7 8 | strong)
[Si Se | involved explicit irrational] → (3 4 5 6 | weak)

sensory formula
[Si Se | involved explicit irrational] → (1 2 7 8 | strong)
[Ne Ni | Detached implicit irrational] → (3 4 5 6 | weak)

Democrat Aristocrat

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

The first gen4 dichotomy, has supralocal formula. Supralocal rule leaves specific positioning of the elements uncertain, but gen4 dichos says something about how the IMEs are placed together. It connects the functions of different nalities using IMEs and FNs blockings.

The first Rule of dem/ari connected it to horizontal Freudian blocking which are very important in socionics. Ego blocking is a quintessence of the TIM it is formed by a combination of 2 IMEs which are connected by specific order of reading them. These are fractal properties of socion again: the element of lvl4 is a combination of 2 elements of lvl3

So horizontal blockings of Democrats and Aristocrats have different combinations of IMEs

Democrats: Intuition+Logic or Sensorics+Ethics
Aristocrats Intuition+Ethics or Sensocrics+Logic

demo/ari connects all the functions that are of the different nality (accepting/producing), these would be 4 blockings in model A which we can describe by their 3 common Fn dichotomies

[1+2, 3+4, 5+6, 7+8] horizonal are equal in (strong/weak | mental/vital | valued/subdued)
[1+4, 2+3, 5+8, 6+7] vertical are equal in (inert/contact | mental/vital | evaluatory/situational)
[1+6, 2+5, 3+8, 4+7] long vertical are equal in (inert/contact | bold/cautious | valued/subdued)
[1+8, 2+7, 3+6, 4+5] dimensions are equal in (strong/weak | evaluatory/situational | bold/cautious)
So depending on demo/ari TIMs would have certain IEs in these blockings, the elements would have specific dichotomies in common, which is shown in parenthesis:
—Democrats—
Horizontal: (Detached /involved | static/dynamic | alpha/gamma)
Vertical: (implicit/explicit | static/dynamic | delta/beta)
Long Vertical: (implicit/explicit | alpha/gamma | extra/intro)
Dimensions: (Detached /involved | delta/beta | extra/intro)

[Ne Ti ~ Se Fi ~ Si Fe ~ Ni Te] → (1 2 ~ 3 4 ~ 5 6 ~ 7 8 | horizontal)
[Ne Fi ~ Se Ti ~ Si Te ~ Ni Fe] → (1 4 ~ 2 3 ~ 5 8 ~ 6 7 | vertical)

[Ne Fe ~ Ti Si ~ Se Te ~ Fi Ni] → (1 6 ~ 2 5 ~ 3 8 ~ 4 6 | long vertical)
[Ne Te ~ Ti Ni ~ Se Fe ~ Fi Si] → (1 8 ~ 2 7 ~ 3 6 ~ 4 5 | dimension)

—Aristocrats—
Horizontal: (implicit/explicit | static/dynamic | delta/beta)
Vertical: (Detached /involved | static/dynamic | alpha/gamma)
Long Vertical: (Detached /involved | delta/beta | extra/intro)
Dimensions: (implicit/explicit | alpha/gamma | extra/intro)

[Ne Fi ~ Se Ti ~ Si Te ~ Ni Fe] → (1 2 ~ 3 4 ~ 5 6 ~ 7 8 | horizontal)
[Ne Ti ~ Se Fi ~ Si Fe ~ Ni Te] → (1 4 ~ 2 3 ~ 5 8 ~ 6 7 | vertical)

[Ne Te ~ Ti Ni ~ Se Fe ~ Fi Si] → (1 6 ~ 2 5 ~ 3 8 ~ 4 6 | long vertical)
[Ne Fe ~ Ti Si ~ Se Te ~ Fi Ni] → (1 8 ~ 2 7 ~ 3 6 ~ 4 5 | dimension)

Ne	Si	Fe	Ti
Te	Fi	Se	Ni

Positivist/Negativist

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

positivist
[Ne Te ~ Fe Se ~ Si Ti ~ Fi Ni] → (1 8 ~ 2 5 ~ 3 6 ~ 4 7)
[Ne Fe ~ Te Se ~ Si Fi ~ Ti Ni] → (1 6 ~ 2 7 ~ 3 8 ~ 4 5)

negativist
[Ne Fe ~ Te Se ~ Si Fi ~ Ti Ni] → (1 8 ~ 2 5 ~ 3 6 ~ 4 7)
[Ne Te ~ Fe Se ~ Si Ti ~ Fi Ni] → (1 6 ~ 2 7 ~ 3 8 ~ 4 5)

To form compatible with this formula tetrachotomy we’ll have to use Gulenko-Newman Dichotomies

phi - ro - vertness

Ne	Si	Fe	Ti
Te	Fi	Se	Ni

pi omega vertness

Ne	Si	Fe	Ti
Te	Fi	Se	Ni

→
(1258 | energetic) x (1368 | vert) x (1478 | tensioned) = (16 | 27 | 38 | 45)

Another way to form such equivalence is to investigate its connection with democrat/aristocrat and vertness formula

instead of demo/ari equivalence +/- use only the two which are equivalent by vertness (bold/cautious for functions)

Since they are equivalent the multiplication by vertness doesnt apply bold functions, but for cautious there would be different partitions as demo/ari switched

It works the same way for Asking/Declaring but using tality instead of vertness

yielding/obstinate

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

yielding formula
[Te Fi | delta gamma rational] → (1 4 5 8 | evaluatory)
[Ti Fe | beta alpha rational] → (2 3 6 7 | Situational)

obstinate formula
[Ti Fe | beta alpha rational]→ (1 4 5 8 | evaluatory)
[Te Fi | delta gamma rational] → (2 3 6 7 | Situational)

eL2
eL1
	eL2
	eL1

Logic/Ethic

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

logic
[Te Ti | Detached Explicit Rational] → (1 2 7 8 | Strong)
[Fe Fi | Involved Implicit Rational] → (3 4 5 6 | Weak)

ethic
[Fe Fi | Involved Implicit Rational] → (1 2 7 8 | Strong)
[Te Ti | Detached Explicit Rational] → (3 4 5 6 | Weak)

		Fe	Ti
Te	Fi

Merry/Serious

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

Merry
[Ti Fe | beta alpha rational]→ (1 2 5 6 | Valued)
[Te Fi | delta gamma rational] → (3 4 7 8 | Subdued)

Serious
[Te Fi | delta gamma rational] → (1 2 5 6 | Valued)
[Ti Fe | beta alpha rational] → (3 4 7 8 | Subdued)

Constructivist/Emotivist

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

constructivist formula
[Fe Fi | Involved Implicit Rational] → (1 4 6 7 | Inert)
[Te Ti | Detached Explicit Rational] → (2 3 5 8 | Contact)

emotivist formula
[Te Ti | Detached Explicit Rational] → (1 4 6 7 | Inert)
[Fe Fi | Involved Implicit Rational] → (2 3 5 8 | Contact)

		Fe	Ti
Te	Fi

10. Process/Result

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

Junginan Faculties (macroelements)

Ne	Si	Fe	Ti
Te	Fi	Se	Ni

semitacts

Direction of the flow in semitacts

process
[Ne Ni > Te Ti > Se Si > Fe Fi | Faculty] → (1 7 > 2 8 > 3 5 > 4 6 | tacts)

result
[Ne Ni > Fe Fi > Se Si > Te Ti | Faculty] → (1 7 > 2 8 > 3 5 > 4 6 | tacts)

11. asking declaring

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

asking
[Ne Ti ~ Si Te ~ Fe Ni ~ Fi Se] → (1 2 ~ 3 4 ~ 5 8 ~ 6 7)
[Ne Fi ~ Si Fe ~ Ti Se ~ Te Ni] → (1 4 ~ 2 3 ~ 5 6 ~ 7 8)

declaring
[Ne Fi ~ Si Fe ~ Ti Se ~ Te Ni]→ (1 2 ~ 3 4 ~ 5 8 ~ 6 7)
[Ne Ti ~ Si Te ~ Fe Ni ~ Fi Se] → (1 4 ~ 2 3 ~ 5 6 ~ 7 8)

[Ne Ti ~ Si Te ~ Fe Ni ~ Fi Se]

Ne	Si	Fe	Ti
Te	Fi	Se	Ni

(12 ~ 34 ~ 58 ~ 67)

[Ne Fi ~ Si Fe ~ Ti Se ~ Te Ni]

Ne	Si	Fe	Ti
Te	Fi	Se	Ni

(14 ~ 23 ~ 56 ~ 78)

Another way to form such equivalence is to investigate its connection with democrat/aristocrat and tality (static/dynamic) formula

instead of demo/ari equivalence ?/! use only the two which are equivalent by static/dynamic (mental/vital for functions)

Since they are equivalent the multiplication by tality doesnt apply mental functions, but for vital there would be different partitions as demo/ari switched

It works the same way for Positivist/Negativist but using vertness instead of tality

12. judicious/decisive

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

judicious
[Ne Si | delta, alpha, irrational] → (1 2 5 6 | verbal)
[Ni Se | beta, gamma, irrational] → (3 4 7 8 | subdued)

decisive
[Ni Se | beta, gamma, irrational]→ (1 2 5 6 | verbal)
[Ne Si | delta, alpha, irrational]→ (3 4 7 8 | subdued)

Ne	Si
		Se	Ni

13. tactical/strategic

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

tactical
[Ne Ni | Detached implicit irrational] → (1 4 6 7 | Inert)
[Si Se | involved explicit irrational] → (2 3 5 8 | Contact)

strategic
[Si Se | involved explicit irrational] → (1 4 6 7 | Inert)
[Ne Ni | Detached implicit irrational] → (2 3 5 8 | Contact)

14. Nality (Irrational/Rational)

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

IrrationalFormula
[Ne Si Se Ni | irrational] → (1 3 5 7 | accepting)
[Fe Ti Te Fi | rational] → (2 4 6 8 | producing)

Rational Formula
[Fe Ti Te Fi | rational] → (1 3 5 7 | accepting)
[Ne Si Se Ni | irrational] → (2 4 6 8 | producing)

15. Tality (static/dynamic)

ILE	SEI	ESE	LII
EIE	LSI	SLE	IEI
LIE	ESI	SEE	ILI
IEE	SLI	LSE	EII

Static
[Ne Ti Fi Se | Static] → (1 2 3 4 | Mental)
[Si Fe Te Ni | Dynamic] → (5 6 7 8 |Vital)

Dynamic
[Si Fe Te Ni | Dynamic] → (1 2 3 4 | Mental)
[Ne Ti Fi Se | Static] → (5 6 7 8 |Vital)