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http://creativecommons.org/licenses/by-sa/4.0/ 0. Introduction

The greatest problem in modern socionics is that it is not scientific. In its current form, socionics is difficult to falsifiable, there are no experiments that can be replicated on a mass scale and there is no standardized methodology. This is evident in the inconsistent typing of celebrities by professional socionists. If socionics is true, every person has a single type their whole lives. The fact that professionals regularly disagree means that either the theory of socionics is wrong, or that many professionals are mistaken. On some level, the socionics community needs an objective standard, which outlines the minimum sufficient evidence required to make a diagnosis and which also gives a degree of confidence. However, due to the complexity of socionics, there are many different paths to determining type. Even if clear standards are developed, the diversity of methods would make it hard to debate and come to a consensus. This is compounded by the fact that there are different schools of socionics that agree they are defining the same sixteen types but use completely different models to do so.

The solution is to reduce the different theories and approaches into simple traits that everyone can agree on. There may be many ways to accomplish this, but the most obvious is to use the existing dichotomy structure that reduces everything into binary traits which is already fully integrated in the theory of socionics.

Dichotomies have two aspects: structural and empirical. Structurally, dichotomies show how concepts relate to each other. Even if dichotomies lack a useful definition, they can be used as simple groups and mathematically keep track of how complex ideas relate to each other. Since model A was created in a logical and consistent way, every part can be represented as combinations of dichotomies. This also allows two models to be broken down and compared piece by piece, acting as a bridge between different schools of thought in socionics.

Accepting socionics requires accepting the structural nature of dichotomies, but not their current empirical definitions. This paper will not focus much on this debate, but it will show how each Reinin dichotomy is related to a combination of information elements and functions in model A and how more accurate and robust definitions could be created with this in mind. If dichotomies can be defined in terms of information metabolism, it will be the first step in making model A testible.

Unlike most psychology theories, socionics does not just rate individuals on a set of scales, but predicts additional traits. A huge potential for this property is to use it as a self-correcting system. It is possible to analyze a set of partially correct traits and determine what information is most likely wrong. In a clinical 2

setting, the practitioner can then double check those traits to try to resolve the error. In the case of inconsistent celebrity typings, the aggregate data from many people can be compared to reveal the most consistent and controversial traits and then focus energy on resolving the controversy: the more information that supports a type, the more confident the diagnosis. Limiting research to individuals who score highly consistent will normalize socionics experiments and make them replicable.

This property of interdependent traits can additionally make socionics falsifiable. Until research can be conducted into a more objective measurement of information metabolism, such as Dario Nardi’s brain imaging of Myers Briggs types, socionics can only be proved indirectly. From the fifteen Reinin dichotomies, there are about thirty three thousand possible combinations but only sixteen possible types. If it can be proved that these dichotomies appear in clusters predicted by the sixteen types and are not random, this is a good step toward statistically validating correlations predicted by socionics.

The internal consistency of dichotomy measurements can also validate or falsify a specific test. Even if good reliable definitions for each dichotomy are created, there still needs to be a way for a subject to fail the evaluation. There are many reasons that may lead to a person to not being in the right state of mind to be evaluated and there must be a way to test for these errors and measure how conclusive the test is.

Assuming such a method can be established and tested, this would create a tool that will greatly increase the accuracy of type diagnosis among all who practice socionics. As it stands, there are a lot of very promising hypotheses in socionics that are only waiting to be rigorously tested, such as the current definitions of the Reinin dichotomies and the small groups pioneered by both Reinin and Gulenko.

Unfortunately, few people understand how this structure works, leaving the dichotomies and small groups confusing and unrelatable. In the English socionics community, almost no one understand how the Reinin dichotomies are generated, how model A relates to dichotomies, how small groups work, or really anything outside of the basic rules for positioning information elements within model A. This isn’t their fault. To formally understand the structure requires knowing abstract algebra and group theory. Not many psychologists are also mathematicians.

A few years ago, in my own attempt to teach myself the theory of small groups; I created a diagram that made understanding the relationship easy. With more experimenting, I found that every aspect in socionics can be understood with these diagrams. Anyone can learn the basic rules for operating them, and once they do, the entire structure of socionics will make sense. The diagrams take the structural properties of socionics and convert them into a physical object which works by nature of spatial relationships and requiring no knowledge of math to use correctly.

If these diagrams are adopted and taught by the establishment, it will have the effect of making everyone who understands them completely literate in the structure of socionics. This is the first step in realizing the potential use of the systematic approach of socionics and making a scientific methodology.

This paper is dedicated to explaining how this diagram method works, using it to understand the structural relationships that already exist in classical socionics and then applying their properties to experiment design. This paper will first illustrate how this diagram method works by examining the Reinin Dichotomies, next show how the Reinin dichotomies are connected to Model A, then reduce the entire theory into structural components and create a master map of all of socionics and finaly conclude by applying all this knowledge to experiment and test design. 3

Table of Contents

0. Introduction ...... 1 1. Diagram Method ...... 4 Basic Theory ...... 4 Dichotomies and Tetrachotomies...... 4 Generating Reinin Dichotomies from Jungian Dichotomies ...... 5 Falsifying Claims with the Identity Element ...... 6 Notating the Sixteen Type Dichotomies ...... 6 Properties of Tetrachotomies and Small Groups ...... 7 Fano Plane Diagrams ...... 9 Constructing a Fano Plane ...... 10 Properties of a Fano Plane ...... 10 A Fano Plane with Type Dichotomies ...... 11 Solving for Additional Traits ...... 11 Groups in Socionics with Eight Elements ...... 13 The Eight Functions and Information Elements Represented with Fano Planes ...... 13 Summary of Fano Planes...... 15 Pyramid Diagrams ...... 16 Constructing a Fano Pyramid ...... 16 Pyramid Color Scheme ...... 17 Location of Each Dichotomy on the Pyramid ...... 17 Complete Pyramid Diagram for the Jungian and Reinin Dichotomies...... 20 Location of Each Tetrachotomy on the Pyramid ...... 21 Using Reinin Dichotomies and Pyramid Diagrams to Solve for Type ...... 25 The Sixteen Types in Pyramid Form ...... 27 Parity Dichotomies and Error Correction ...... 28 How Parity Dichotomies Reduce False Positives...... 29 Error Correcting a Hypothetical Test Result ...... 31

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1. Diagram Method

Basic Theory

Everything in Model A comes down to two basic concepts: dichotomies and tetrachotomies. Understanding these two concepts allows anyone to use the diagrams presented in this paper and in turn, understand and manipulate every concept in Model A. Even the most complicated structures are simple when they are broken down into these parts. This first section will examine the properties of dichotomies and tetrachotomies, and then will show how they can be graphed as a block design.

Dichotomies and Tetrachotomies

A dichotomy is simply a category that divides a group into two separate classes. In socionics, each of these parts is the same size, so a dichotomy that divides a group of sixteen elements would have two halves of eight elements. The most famous and accepted dichotomies are the four Jungian dichotomies adapted from Jung’s own system to fit socionics. Each Jungian dichotomy divides the sixteen types into two unique groups of eight types.

Two dichotomies can intersect to make a tetrachotomy, which divides a group into four small groups, each of which includes four types. For example, the temperament small groups can be created by intersecting the {extrovert, introvert} dichotomy with the {irrational, rational} dichotomy.

Extrovert types Introvert types Flexible-Maneuvering Receptive-Adaptive Irrational types ILE, IEE, SLE, SEE ILI, IEI, SLI, SEI Linear-Assertive Ridged-Stable Rational types LIE, EIE, LSE, ESE LII, EII, LSI, ESI

Tetrachotomies are fundamental to socionics. The three most famous are club, quadra and temperament, but many more exist. They also exist in all areas of the theory. The mental blocks, Ego, Superego, Id and Super-id, are all small groups of function dichotomies, and the dual pairs of elements IS, FT, EL and PR are small groups of information element dichotomies.

The club and temperament tetrachotomies can be constructed with two Jungian dichotomies, but there is no way to combine two Jungian dichotomies to get quadra. This is where Reinin’s dichotomies become necessary. Quadra can be defined by the {judicious, decisive} dichotomy and {merry, serious} dichotomies. This makes sense because judicious types value S+I, decisive types value F+T, merry types value E+L and serious types value P+R.

Judicious Decisive (values I+S) (values F+T) Merry Alpha Beta (values E+L) ILE, ESE, LII, SEI EIE, SLE, IEI, LSI Serious Delta Gamma (values P+R) IEE, LSE, EII, SLI LIE, SEE, ILI, ESI

It’s worth noting briefly that not everyone believes the current definitions of the Reinin dichotomies or 5

small groups are useful or accurate. That debate is separate to how they will be used in this section: as structural elements. Once the structure is understood; a debate about the empirical content of each will be much more productive. Later in this paper, the type dichotomies will be related to concepts in model A, creating the potential that every dichotomy, even the four Jungian, may be redefined in terms of information metabolism.

Generating Reinin Dichotomies from Jungian Dichotomies

Each eleven Reinin dichotomy can be generated from the four Jungian dichotomies. This does not mean they are any better or more advanced than the original four, just that they can be derived using simple logic. The Reinin dichotomies still divide the sixteen types into two groups of eight types. It is even possible to start with four Reinin dichotomies and generate the Jungian dichotomies from them!

The generation of Reinin dichotomies can be understood with tetrachotomies. As previously shown, the intersection of two dichotomies creates a tetrachotomy of four small groups. Using the abstract dichotomies A{+,–} and B{+,–}, four small groups can be created and numbered one through four.

B+ B– A+ 1 2 A– 3 4

Now that the numbered small groups have been defined, there are three ways to recombine pairs of small groups into dichotomies. The first two are the original A and B dichotomies, but the third is a new dichotomy call AB, because it was generated from A and B. AB does not define new types of information metabolism, it only rearranges the existing small groups. A way to picture this relationship is by imagining all the ways four people can shake hands at once.

A+ 1 2 B+ B– AB+ AB– 1 2 1 2 3 4 4 3 A– 3 4

Reinin dichotomies are generated in the same way. They are created as a third way of pairing small groups in a dichotomy intersection. The third dichotomy in the temperaments small group is the {static, dynamic} Reinin dichotomy. This dichotomy gets its name from the kind of information elements in the first four “mental” functions of each type: all the flexible-maneuvering and ridged-stable types have static mental functions and all the linear-assertive and receptive-adaptive types have dynamic mental functions.

Extrovert Introvert Static Dynamic Irrational Flexible-Maneuvering Receptive -Adaptive ILE, IEE, SLE, SEE ILI, IEI, SLI, SEI Dynamic Static Rational Linear-Assertive Ridged-Stable LIE, EIE, LSE, ESE LII, EII, LSI, ESI

Now that the {static, dynamic} dichotomy is generated, intersecting it with the {intuitive, sensory} dichotomy creates the small group defined as romance styles by Victor Gulenko and a new dichotomy, 6

{judicious, decisive}, one of the dichotomies needed for quadra. Just like dichotomies, tetrachotomies are logical relationships that exist regardless of a good description.

Intuitive Sensory Judicious Decisive Static Infantile Aggressor ILE, IEE, LII, EII SLE, SEE, LSI, ESI Decisive Judicious Dynamic Victim Caregiver LIE, EIE, ILI, IEI LSE, ESE, SLI, SEI

Continuing to combine dichotomies with each other to generate new dichotomies will eventually produce a total of sixteen dichotomies, at which point any combination will result in a dichotomy already generated. Four of these dichotomies are the original Jungian dichotomies, eleven are the Reinin dichotomies and the last one is called identity, which is technically the twelfth Reinin dichotomy. It results when any dichotomy is combined with itself. Here is an example of generating the {valid, null} identity dichotomy using the {logics, ethics} dichotomy.

Logic Ethics Valid Null Logic ILE, LIE, SLE, LSE ILI, LII, SLI, LSI Null Valid Ethics IEE, EIE, SEE, ESE IEI, EII, SEI, ESI

Falsifying Claims with the Identity Element

Identity is one of the most interesting but under-explored dichotomies. A major hypothesis in socionics is each person must be one type or another. A way to falsify this claim is to show that a person could be both or neither. Using this example of generating the identity element with the {logic, ethics} dichotomy, socionics is claiming that a person must be either a logical or ethical type but never both. Finding a person who is both or neither proves this claim false and invalidates the {logic, ethics} dichotomy. At least four dichotomies must be proven with the identity element to prove the socionics typology.

Notating the Sixteen Type Dichotomies

Below is a table of all 16 type dichotomies. The first dichotomy 1 is the identity element, the next four are the Jungian dichotomies, and the remaining eleven are the Reinin dichotomies. The Jungian dichotomies are represented by the letter code for ILE, ENTp, which is the base type. Any of the sixteen types can be the base, and since no one has an advantage over another, ILE was selected to honor Augusta. The multi letter codes for the Reinin dichotomies do not relate to a certain type code, but instead are recipes of how to create them from combinations of Jungian dichotomies. Jungian dichotomies can be combined in any order and still result in the same Reinin dichotomy. The two traits in each dichotomy are represented as a plus or minus charge, where the plus trait is always an ILE trait. 7

This is so the positive traits for the four Jungian dichotomies are associated with the letter code for ILE: E+ is extrovert, N+ is intuitive, T+ (T for thinking) is logical and P+ (P for perceiving) is irrational.

+ – + – 1 Valid Null NT Democratic Aristocratic E Extrovert Introvert NP Tactical Strategic N Intuitive Sensory TP Constructive Emotive T Logical Ethical ENT Positivist Negativist P Irrational Rational ENP Judicious Decisive EN Carefree Farsighted ETP Merry Serious ET Yielding Obstinate NTP Process Results EP Static Dynamic ENTP Asking Declaring

Properties of Tetrachotomies and Small Groups

To summarize, each tetrachotomy is made of four small groups that can be defined with three dichotomy traits. When put into a table, these dichotomies are horizontal, vertical and crossed pairs. Any two of these three dichotomies can construct the tetrachotomy which generates the third dichotomy.

Any three small group dichotomies are a dependent system. This means that while there are eight (23) different ways to combine the traits, there are only four possible small groups. Defining two traits defines one of the four small groups and since each small group is defined by three dichotomy traits, also defines the third trait. Using the temperament small groups as example, an extravert and irrational type is a member of the flexible-maneuvering temperament, making it a static type. A dynamic and introverted type is a member of the receptive-adaptive small group, making it an irrational type, etcetera.

E+ Extrovert E– Introvert EN+ Static EN– Dynamic N+ Irrational Flexible-Maneuvering Receptive-Adaptive ILE, IEE, SLE, SEE ILI, IEI, SLI, SEI EN– Dynamic EN+ Static N– Rational Linear-Assertive Ridged-Stable LIE, EIE, LSE, ESE LII, EII, LSI, ESI

The other four combinations of traits are impossible. An example of an impossible combination is a rational, extroverted and static type. Extrovert and rational together is the Linear-Assertive temperament, which is by definition dynamic, not static. This means this combination does not exist because no type is both static and dynamic.

Extravert Static & = Null Rational Linear-Assertive Static

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This pattern of four possible and four impossible dichotomy trait combinations can be generalized to all small groups.

Possible Impossible * B+ B- A B AB A B AB A+ AB+ AB– 1 + + + Ø + + – 1 2 2 + – – Ø + – + A- AB– AB+ 3 – + – Ø – + + 3 4 4 – – + Ø – – –

There are two quick and easy ways to determine if the combination of three small group traits is possible. The first way uses the multiplication property of positive and negative charges. The charges of any two dichotomies can be multiplied to determine the charge of the third dichotomy in the triad. So if two dichotomy charges multiply and equal the third charge, it is a valid combination and if not, it is an impossible combination. From the tables above, it can be seen that all valid combinations have an odd number of positive traits, while impossible combinations have either zero or two positive traits. The second way to evaluate three traits is to count the positive charges. If there are an odd number of positive traits, it is valid, and if not, it is impossible.

Any small group can be written in these two styles of tables. For example, below is the temperament small group. The table style on the left is nice because it shows the construction of the third dichotomy, making it intuitively easier to understand why the dichotomies relate, and what combination of dichotomies is valid. The table on the right is nice because it shows that all three dichotomies are mathematically equal, there is no hierarchy of traits, and it is easier to evaluate if there are an odd or even number of positive traits.

Extrovert (E+) Introvert (E-) P E EP Irrational Static (EP+) Dynamic (EP-) + + + (P+) Flexible-Maneuvering Irrational Extrovert Static Flexible Receptive + – – Maneuvering Adaptive Receptive-Adaptive Irrational Introvert Dynamic Rational Dynamic (EP-) Static (EP+) – + – (P-) Linear-Assertive Rational Extrovert Dynamic Linear Ridged – – + Assertive Stable Ridged-Stable Rational Introvert Static

This is all the background required to understand the diagrams. To summarize, a combination of any two of the fifteen Jungian/Reinin dichotomies creates a tetrachotomy with four small groups of four types. This tetrachotomy is always defined by a third dichotomy and any two of these three dichotomies is enough information to define one of the four small groups. Each small group is defined by all three traits, so by defining a small group with two dichotomy traits necessarily defines a third trait. The dichotomies that describe ILE are always positive and the others are always negative. In a valid combination of trait, multiplying the charges of any two dichotomies will result in the charge of third dichotomy, resulting in an odd number of positive traits. Positive traits are often shaded for visual clarity.

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Fano Plane Diagrams

Just as the two basic elements in socionics are dichotomies and tetrachotomies, the two basic elements in a diagram are points and lines. Each point represents a dichotomy, and each line represents a tetrachotomy. Since there are three dichotomies per small group, there are always three points on each line.

Diagram Dichotomy Tables The whole tetrachotomy without A AB B B+ B- any small group defined. #1 + + + A+ AB+ AB- A AB B #2 + – – #1 #2 #3 – – + A- AB- AB+ #3 #4 #4 – + –

The four small groups defined by These diagrams have been their three traits. For these to be rearranged for compactness, but valid, there must be an odd still include the small group number of positive traits member number top left.

#1 B+ A AB B A AB B A+ AB+ #1 + + +

#2 B- A AB B A AB B A+ AB- #2 + – –

#3 B+ A AB B A AB B #3 – – + A- AB-

#4 B- A AB B A AB B #4 – + – A- AB+

Representing a single small group as a diagram is not more useful than representing it with a table. However, the power of these diagrams becomes clear when working with complex systems of multiple small groups which would be incredibly overwhelming and confusing if they were represented as tables. At any point, the tetrachotomy or small group drawn in the graphed form can be substituted with a regular table.

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Constructing a Fano Plane

This construction adds a third independent dichotomy, C, to the tetrachotomy constructed from A and B

A 1 First, C is placed to form an equilateral triangle when connected with dichotomies A and B. The exact placement is not that important, more for aesthetics – the diagram this will AB create is called a Fano plane which is normally drawn as an equilateral triangle. B C

A 2 Next, C is combined with A, B and AB to create three small groups and thus, three new dichotomies. These seven dichotomies plus the identity element are all the new dichotomies AB AC that can be formed from A, B and C. ABC

B C BC

A 3 Last, since all possible dichotomies have been generated, the group is closed. This means that any two dichotomies combined will create a small group with the third dichotomy AB AC belonging to one of the existing seven ABC dichotomies. Using this property, the last three small groups are drawn in connecting every B C dichotomy to every other. BC

Properties of a Fano Plane

This diagram is called the Fano plane after Gino Fano, the Italian mathematician who discovered it. Just as a small group can be generated from any two dichotomies, the Fano plane can be generated from any three. This even includes three dependent dichotomies from the same small group, which would only create more of the same dichotomies and the identity element, which is redundant information. For this reason, this high order geometry will almost always start with independent traits, but the structure works either way. 11

Before socionics dichotomies are placed on the + – Fano plane, here is a general geometric example. Each cube represents a dichotomy, having eight bits total and four bit per trait. Colored cube bits are positive and white bits are negative. Each line represents a tetrachotomy. Any two cubes in a small group can be combined by multiplying the charges of each bit to generate the third cube on the same line.

A Fano Plane with Type Dichotomies

For a more concrete example, the N {intuitive, sensory} dichotomy is added to the temperament tetrachotomy. On the left is a simplified diagram with the Reinin type code, and the right has the dichotomy traits and the three known small groups for the space.

E E Extrovert Introvert Stimulus Temperament EN EP ENP EN EP Carefree Static N P Farsighted ENP Dynamic NP Romance Judicious Decisive N NP P Intuitive Tactical Irrational Sensory Strategic Rational

This space is also a subgroup of types. Instead of a tetrachotomy that has four groups of four types, this is an octachotomy which defines eight dyads of two types. Any two types share one identical octachotomy. This space above is shared by irrational kindred relations and rational look-alike relations.

Solving for Additional Traits

This diagram is good for is solving for additional traits that must logically follow from observation and exploring the relationship between different concepts. It can also be used to determine the values of the Jungian dichotomies in the space, which are an easier indication of type.

For example, what types are farsighted, decisive and tactical? 12

The first step is to draw a white E or black circle for each dichotomy given. ILE is not farsighted or decisive, so those traits, EN and ENP, are negative. EN EP ILE is tactical, making NP ENP positive. N P NP Next, the three dichotomies can E be combined in any order. This Undefined NP+ example starts with combining Group Tactical tactical (NP+) with farsighted (EN-) with an undefined group to EN EP form dynamic (EP-). This means ENP that a type that is tactical and farsighted must also be dynamic. N P EN– EP– Farsighted Dynamic NP The small group that is formed E from EP with ENP is Gulenko’s Romance ENP– romance styles. A type that is Styles Decisive both dynamic (EP-) and decisive Infantile Aggressor (ENP-) must be have the victim EN EP romantic style, and making them ENP an intuitive type (N+). This Caregiver Victim member can also be defined as N P EP– N+ having T in their ego block. Dynamic Intuitive NP

The small group that is formed E from N with EN is Gulenko’s Stimulus EN– stimulus group. A type that is Farsighted both intuitive (N+) and Uniqueness Confidence farsighted (EN-) is in the group EN EP N+ E– seeking confidence, meaning ENP Intuitive Introvert they are an introvert (E-). Wellbeing Prestige N P

NP

This last group formed from E combining E with EP is the Tempera- EP– temperament small group. A ment Dynamic type that is introverted (E-) and Flexible Assertive dynamic (EP-) is the receptive- EN EP adaptive temperament, often ENP denoted as IP. This temperament Stable Receptive is irrational (P+), completing all N P E– P+ dichotomies for this space. Introvert Irrational NP

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To summarize, a type that is farsighted, tactical E- and decisive must also be dynamic, intuitive, Introvert introverted and irrational. Using the four letter type code and the derived Jungian dichotomies, Confidence Receptive they are IN_p, where the underscore may either Adaptive be logic or ethics. This defines the kindred pair IEI and ILI, as expected, because this is the kindred EN- EP- dyad for irrational types. Farsighted Dynamic ENP- Once a diagram is solved correctly, every small Victim Decisive group will follow the rule of an odd number of positive traits. N+ NP+ P+ Intuitive Tactical Irrational

Groups in Socionics with Eight Elements

Unlike the sixteen types, a few concepts in socionics have eight elements that can be fully defined with three dichotomies. The two most important groups like this are the information elements and functions. The I1 function for ILE is used as a base, so the positive traits always include either the base function or extroverted intuition and the negative traits are those that do not.

The Eight Functions and Information Elements Represented with Fano Planes

A cool property of Fano planes in socionics is they have eight possible positive – negative settings. Either all dichotomies are positive, or one small group of three traits is positive and the other four traits are negative. Below is a table of the functions defined by their dichotomies, with the all positive small groups in bold. 14

Base Creative Bold Cautious 1 2

Evaluating Mental Situational Mental

Valued Valued

Strong Inert Accepting Strong Contact Producing

Vulnerable Role Cautious Bold

4 3 Evaluating Mental Situational Mental

Subdued Subdue d Weak Inert Producing Weak Contact Accepting

Mobilizing Suggestive Cautious Bold

Evaluating Vital 6 5 Situational Vital Valued

Valued Weak Contact Accepting Weak Inert Producing

Ignoring Demonstrative Cautious Bold

Situational Vital Evaluating Vital 7 8 Subdued Subdued

Strong Inert Accepting Strong Contact Producing

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A similar diagram can be made for the information element, with the eight configurations of positive and negative values corresponding to the eight information elements

Extroverted Extroverted Intuition Extroverted Sensing Extroverted

Δ Valued Static B Valued Static

A Valued Γ Valued

Abstract Internal Irrational Involved External Irrational

Extroverted Extroverted Logic Extroverted Ethics Extroverted

Δ Valued Dynamic B Valued Dynamic

Γ Valued A Valued

Abstract External Rational Involved Internal Rational

Introverted Introverted Intuition Introverted Sensing Introverted

B Valued Dynamic Δ Valued Dynamic

Γ Valued A Valued

Abstract Internal Irrational Involved External Irrational

Introverted Introverted Logic Introverted Ethics Introverted

B Valued Static Δ Valued Static A Valued Γ Valued

Abstract External Rational Involved Internal Rational

Summary of Fano Planes

To summarize, three original dichotomies creates a system of seven dichotomies that can be drawn as a Fano plane. This shape has seven points and seven lines, representing the seven dichotomies and seven small groups between the dichotomies. Each line connects three points and is a small group which can 16

be substituted with a tetrachotomy table. Since they are small groups, all three traits connected by a line are related by the multiplication of positive and negative numbers. Using this property, additional traits can be solved geometrically given a few original dichotomies. When fully solved, there are exactly eight possible combinations of positive and negative traits for every Fano plane. The function and information element dichotomies can be fully modeled with a Fano plane, and the eight possible combinations correspond to the eight functions and elements. For every intertype relation, there is a Fano plane subspace that is identical between the two types.

To fully define the sixteen types, one additional trait is required to distinguish between the two dyad members. This next section describes what a diagram with four original dichotomies looks like, and how to construct it.

Pyramid Diagrams

Constructing a Fano Pyramid

Just as the Fano plane can be constructed from a line and a point, a pyramid diagram can be constructed from a Fano plane and a point.

E 1 Since the Reinin dichotomies are the primary use of this space, these construction will use the Jungian type code E, N, T, P instead of A, B, C and D. The first step is to place the T EN dichotomy next to the Fano plane constructed EP in the previous example from {E,N,P} so that it ENP will form a tetrahedron when T is connected to the other Jungian dichotomies N NP P

T E 2 Next, T is connected to all seven points in the {E,N,P} Fano plane to generate the remaining seven Reinin dichotomies for a total of fifteen. EN EP ET ENP ENT ETP N ENTP NP P NT NTP TP T 17

E 3 These are all fifteen Jungain and Reinin dichotomies, making this group closed. The last ENTP step it to draw in all the remaining tetrachotomy combinations so that every EN dichotomy is connected to every other. This ENT results in 35 tetrachotomies in total, which is too complicated to draw all at once. The diagram on the right has all 25 tetrachotomies N that can be drawn with straight lines but P excludes the 10 that are circles.

T Pyramid Color Scheme

Since a pyramid diagram is considerably more complex than a Fano plane, each point is colored to make it easier to visualize. The outside of the base is a color spectrum with white in the middle. The outside corners are loosely red, green and blue, the additive primaries. Then each side is the printing primaries, cyan, magenta and yellow. The dichotomies in the middle level are darker shades of the dichotomies below them and the top point is black.

Location of Each Dichotomy on the Pyramid

The four corners are the Jungian dichotomies

E E N E + Extrovert + Intuitive - Introvert - Sensory Ep Ej Ip Ij Ep Ej Ip Ij NT ILE LIE ILI LII NT ILE LIE ILI LII NF IEE EIE IEI EII NF IEE EIE IEI EII N N ST SLE LSE SLI LSI P ST SLE LSE SLI LSI P SF SEE ESE SEI ESI SF SEE ESE SEI ESI

T T 18

T E P E + Logical + Irrational - Ethical - Rational Ep Ej Ip Ij Ep Ej Ip Ij NT ILE LIE ILI LII NT ILE LIE ILI LII NF IEE EIE IEI EII NF IEE EIE IEI EII N N ST SLE LSE SLI LSI P ST SLE LSE SLI LSI P SF SEE ESE SEI ESI SF SEE ESE SEI ESI

T T

The six edges are the Reinin dichotomies that can be generated from two Jungian dichotomies

EN E ET E + Carefree + Yielding - Farsighted - Obstinate Ep Ej Ip Ij Ep Ej Ip Ij NT ILE LIE ILI LII NT ILE LIE ILI LII NF IEE EIE IEI EII NF IEE EIE IEI EII N N ST SLE LSE SLI LSI P ST SLE LSE SLI LSI P SF SEE ESE SEI ESI SF SEE ESE SEI ESI

T T EP E NT E + Static + Democratic - Dynamic - Aristocratic Ep Ej Ip Ij Ep Ej Ip Ij NT ILE LIE ILI LII NT ILE LIE ILI LII NF IEE EIE IEI EII NF IEE EIE IEI EII N N ST SLE LSE SLI LSI P ST SLE LSE SLI LSI P SF SEE ESE SEI ESI SF SEE ESE SEI ESI

T T NP E TP E + Tactical + Constructive - Strategic - Emotive Ep Ej Ip Ij Ep Ej Ip Ij NT ILE LIE ILI LII NT ILE LIE ILI LII

NF IEE EIE IEI EII N NF IEE EIE IEI EII N ST SLE LSE SLI LSI P ST SLE LSE SLI LSI P SF SEE ESE SEI ESI SF SEE ESE SEI ESI

T T 19

The four faces are the Reinin dichotomies that can be created from combining three Jungian dichotomies. The order they are combined does not matter.

ENT E ENP E + Positivist + Judicious - Negativist - Decisive Ep Ej Ip Ij Ep Ej Ip Ij NT ILE LIE ILI LII NT ILE LIE ILI LII NF IEE EIE IEI EII NF IEE EIE IEI EII N N ST SLE LSE SLI LSI P ST SLE LSE SLI LSI P SF SEE ESE SEI ESI SF SEE ESE SEI ESI

T T ETP E NTP E + Merry + Process - Serious - Result Ep Ej Ip Ij Ep Ej Ip Ij NT ILE LIE ILI LII NT ILE LIE ILI LII

NF IEE EIE IEI EII N NF IEE EIE IEI EII N ST SLE LSE SLI LSI P ST SLE LSE SLI LSI P SF SEE ESE SEI ESI SF SEE ESE SEI ESI

T T

The center is ENTP, the asking – declaring dichotomy, which is generated from combing all four Jungian dichotomies.

ENTP E + Asking - Declaring Ep Ej Ip Ij NT ILE LIE ILI LII NF IEE EIE IEI EII N ST SLE LSE SLI LSI P SF SEE ESE SEI ESI T

The only dichotomy not in the diagram is the identity element, 1 {valid, null}.

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Complete Pyramid Diagram for the Jungian and Reinin Dichotomies

Here is a large completed diagram with all fifteen type dichotomies.

Now that each Jungian and Reinin dichotomies has been mapped to the pyramid, the next step is to show all possible 35 tetrachotomies.

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Location of Each Tetrachotomy on the Pyramid

There are six tetrachotomies that connect two corners along an edge

Stimulus Communication Style Temperament E E E

N N N P P P

T T T

Club Reasoning E E E

N N N P P P

T T T

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There are twelve tetrachotomies connecting a corner to an edge across a face

E E E

N N N P P P

T T T

Romantic Styles E E E

N N N P P P

T T T E E E

N N N P P P

T T T

Blocking E E E

N N N P P P

T T T

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There are four tetrachotomies that connect a point to the opposite face through the center

Benefit Rings E E E

N N N P P P

T T T

E

N P

T

There are three tetrachotomies that connect opposite edges through the center

E E E

N N N P P P

T T T

These are all twenty five tetrachotomies that can be represented with straight lines; the other ten are circular. Since normally these circular groups will be left out of a diagram for readability, a strategy to find them is to find the subspace they are a part of. There are ten triangular subspaces, and since each subspace is a Fano plane, each has one circle connecting the midpoints of the triangle.

There are four circular tetrachotomies for each face of the tetrahedron, connecting three edges to each other.

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E E E

N N N P P P

T T T

E

N P

T

There are six circular tetrachotomies that connect two faces to an opposite edge.

Supervision Rings E E E

N N N P P P

T T T

Quadra E E E

N N N P P P

T T T

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These are all thirty five tetrachotomies that exist in model A. Together, they connect every dichotomy to every other, illustrating the property of closure.

Using Reinin Dichotomies and Pyramid Diagrams to Solve for Type

As with the dyad example, the immediate application of this diagram is defining type. It takes two independent dichotomies to define a small group, three to define a dyad and four to define a single type. Let’s say a person has tested as decisive, results, farsighted and static: is this type possible and if so, which type?

ILE is static, so that E Visually, no three E trait, EP, is positive. points are on the The other three, same line, meaning decisive, results and they are farsighted are the independent and opposite of ILE, so there is no N N ENP, NTP and EN possibility of P P are negative. conflicting dichotomies. T T E E

+ Static – Farsighted + + – Decisive – Decisive = N = N – Sensory + Irrational

P P

T T E E

+ Irrational + Extrovert + + + Static – Decisive = N = N + Extrovert – Strategic

P P

T T E This type is E extroverted, – Strategic sensory, logic and + irrational: SLE. The – Results diagram to the right has the = N N + Logic solution for the

P P remaining five dichotomies. T T 26

It is also possible to define a type with two independent small groups, like quadra and temperament. The process is essentially the same, each small group is represented by three dichotomies and then the remaining dichotomies are derived from them. For example, what type is a receptive-adaptive temperament (Ip) and in the Gamma quadra?

Each small group is E E converted into dichotomies and – Dynamic placed as charges + on a pyramid – Decisive diagram: receptive- N = N adaptive is the + Intuitive

P P right edge and Gamma, the circle. T T E This type is E introverted, – Dynamic intuitive, logical + and irrational, – Serious meaning ILI. The remaining seven = N N + Logic dichotomies have

P P been filled in. T T

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The Sixteen Types in Pyramid Form

Just as the eight possible arrangements of charges on the Fano plane corresponds to an information element or function, the sixteen possible pyramids each corresponds to one of the sixteen types. Since ILE is the base type, it is the only pyramid that has all positive traits. All other fifteen types have seven positive traits (plus identity for a total of eight positive traits) and eight negative traits. The seven positive traits make a unique Fano plane which can be used to visually identify and remember each type. There are ten triangular planes, four conical planes and one sphere.

ILE – ENTp LIE – ENTj ILI – INTp LII – INTj

IEE – ENFp EIE – ENFj IEI – INFp EII – INFj

SLE – ESTp LSE – ESTj SLI – ISTp LSI – ISTj

SEE – ESFp ESE – ESFj SEI – ISFp ESI – ISFj

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Parity Dichotomies and Error Correction

Now that it has been shown how type can be generated from four independent dichotomies or two independent small groups (and by extension a small group and two dichotomies), let’s explore dependent traits. It may seem that dependent traits are unnecessary because they are redundant and either confirms or conflicts with an initial observation, but it is exactly this quality that makes them useful.

In data communication, parity bits are used as basic error correction. At the end of a line of bits, an additional number is added representing if there is and even or odd number of 1s. If one bit is distorted, the parity bit will not match the line of code received and signal an error. It would take two errors to appear as correct code, which is much more unlikely that a single error. For more advanced algorithms, it is possible to use multiple parity bits to not only make it rare for an error to pass unnoticed, but to reconstructed the broken section of code.

Dependent dichotomies have this same potential for socionics typing. The data in this case is the unseen mental architecture of a person’s mind that must be communicated through a test or interview. In either case, there are many places for the signal to be distorted; most people are unaware of the inner workings of their mind and are notoriously unreliable, environmental factors such as distractions and strong emotions may push someone outside of their baseline state, the test or practitioner may ask the wrong questions or misinterpret the answers or just the complexity and uniqueness of personality may not be encapsulated in the test. All of these factors add up to make legit personality testing tenuous.

A perfect example is the American sister theory to socionics, the Myers Brigg Type Indicator, that rates people on four Jungian dichotomies. For each dichotomy, there are many questions that mean about the same thing that are averaged together to give strength of preference. This statistically weeds out random answers, but has nothing to double check bias. The United States is a very social society. Initiative, confidence and sociability are desirable traits and people who are too quiet or reserved are seen as insecure and unsuccessful. This social pressure encourages many introverts to learn to appear more extroverted than they would naturally be. If the hypothesis in socionics is true, then a type of information metabolism is static for a person’s entire life – social pressure will never be enough to change hard brain wiring. When an introvert takes the MBTI, it is possible he has learned to be social (MBTI conflates extroversion with sociability) or may feel he at least should be extroverted (such as in a job assessment), and skew the results to be neutral or even type as an extrovert. Another example could be an ethical male, who has learbed to see the world scientifically and rationally, and devalue his emotions for the sake of a masculine mindset. Such a person may test as a thinker (analogous to logical) rather than a feeler. In both cases, there is no system in the Myers Briggs to contradict these seemingly consistent test answers and diagnoses the wrong type.

Testing someone based on behavior rather than information metabolism may actually be advantageous in a business context. The employer is not trying to understand his employees’ souls, all he cares about is how to maximize their efficiency. If someone is social, for whatever reason, put them with people; if they like to solve problems (maybe an ethical type who has tested as a thinker) give them problems. This inaccuracy, however, is completely unacceptable for socionics because the main application of socionics is intertype relations, which change dramatically for each type combination.

The greatest potential of parity dichotomies is the ability to realize when an assessment is inconclusive. If a monkey is put in front of a keyboard, there must be a way to prove that test is not accurate. Such an approach is unprecedented in psychology because most of psychological tests are purely empirical and 29

are not able to cross check their results internally except with a statistical average. If applied correctly, the structure of socionics may give it the leverage to establish itself as the standard test of Jung’s typology.

The most basic system that can use parity bits as error correction is a small group. As mentioned earlier, there are four possible and four impossible combinations of small group dichotomies. Defining the first two selects a small group, and the third dichotomy either confirms or denies this selection. Since the third dichotomy adds parity to the system, it is much more unlikely to result in a false positive.

How Parity Dichotomies Reduce False Positives.

Let’s examine the probability of defining a small group member using two independent dichotomies verses a dependent system of three dichotomies, with a tree diagram. For this example, the probability of getting any of the dichotomies wrong is 1 out of 10. The following is the probability of using two independent dichotomies. T stands for the true, or correct diagnosis and F is false, or incorrect. The final probability of each leaf of the tree is equal to the number on each branch in the path multiplied together.

A B P of all P of a false correct positive

TT .81 T .9 .9 .1 TF .09 0 .1 FT .09 F .9 .1 FF .01

Totals .81 .19

Because there is no parity in this system, getting one or both traits wrong looks as legitimate as the correct type. It is still much more probable to get the right answer (81%) but about one in every five time, the type will be misdiagnosed (19%) and return a false positive. If all four dichotomies being used for type are as accurate, then a third of people who take the test will be assigned the wrong type (34%).

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Using the third dichotomy in the small group makes things a little more interesting.

Error Error Detected Detected A B AB P of all P of one P of two wrong, P of all correct wrong a false positive wrong

TT .9 TTT .729 T .9 .1 TTF .081 .1 TF .9 TFT .081 .9 .1 TFF .009 FT .9 FTT .081 .1 F .9 .1 FTF .009 .1 FF .9 FFT .009 .1 FFF .001

Totals .729 .243 .027 .001

Surprisingly, including all three dichotomies slightly decreases the chances of correctly diagnosing type (from 81% to 73%) which makes sense because the third dichotomy also has a 10% chance of being wrong and contradicting a correct combination of the first two dichotomies. The reason this system is so much better than with two dichotomies is because the chances of getting a false positive is much lower (from 19% to 3%). Since a system of small group dichotomies must always have an odd number of positive traits, getting one incorrect creates an impossible combination that can be detected. It is only when two traits are incorrect that it appears to be consistent and returns a false positive. This means that when the three traits are consistent, there is 96% confident that the diagnosis is correct, which is an improvement over 81% when only two dichotomies are used.

In the case of a three consistent dichotomies: Probability of a correct positive: .729/(.729+.027) = .964 Probability of a false positive: .027/(.729+.027) = .036

These numbers, of course, are dependent on the actual probabilities of each dichotomy. The more accurate a dichotomy, the more valuable it is. There comes a point when a dichotomy is so inaccurate that it becomes useless and harmful to the system. A probability tree diagram like the one above can be used to calculate the actual accuracy of three dichotomies in a small group by changing the probabilities on each column of branches to be the accuracy of each of the three dichotomies.

Possibilities When an Error is Detected

Now that it has been shown that using three dichotomies greatly increases the accuracy of a possible diagnosis, consider a case when an error is detected. To do this, let’s look at a more concrete example using the temperament small group. Suppose initially, a person seems to be extroverted and irrational, making them the flexible maneuvering temperament. Then upon further analysis, this person appears to be dynamic, which is a trait that contradicts the flexible maneuvering temperament. In this case, at least one dichotomy is wrong.

The most likely error is only one of the three dichotomies are wrong. If extroversion is wrong, the person is the Ip, the receptive adaptive temperament. If irrationality is wrong, the person is Ej, the liner- 31

assertive temperament. If static is wrong, then the person is what was originally thought, Ep, the flexible- maneuvering temperament. If all three dichotomies are wrong and the person is the polar opposite of what is observed, then the person is Ij, the rigid – stable temperament. Here is a table of the four possible temperaments and their associated probabilities continuing the example of a one in five chance any dichotomy could be wrong

Irrational Rational Extrovert Static Dynamic Flexible - Maneuvering Linear - Assertive Probability: .332 Probability: .332

Introvert Dynamic Static Rigid - Stable has Receptive - Adaptive Rigid - Stable the lowest Probability: .332 Probability: .004 probability, less than half a percent

From this table, it is clear that whatever type this person is, they are probably not rigid - stable. This shows that even in the case of a partial mistype, there is still useful information in what a person is not.

The next step is to cross check these three dichotomies against other dependent systems, or to reexamine the original observations and prove one wrong. This process is holistic, because the dichotomies that are being uses as parity information are also being tested themselves against every other dichotomy.

Error Correcting a Hypothetical Test Result

To visualize this process, imagine these fifteen dichotomy traits have been observed, and they are being analyzed to find inconstancies with a pyramid diagram.

E+ Extrovert EN- Farsighted NP- Strategic ETP+ Merry N+ Intuitive ET+ Yielding TP- Emotivist NTP- Results T+ Logical EP- Dynamic ENT+ Positivist ENTP+ Asking P+ Irrational NT- Aristocratic ENP- Decisive

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At first glance, it may be tempting to say this person is ENTp, ILE, but further investigation show that this is not certain, too many of the dichotomies are the opposite of ILE (negative).

The error correction process is fairly simple although labor intensive. It requires checking every dichotomy against every other to uncover which traits are likely true and which are likely false.

Below is the complete process for scoring extroversion. In the future, the algorithm can be tweaked to weight which dichotomies are more reliable than other, but for this example, each dichotomy is equal. If a dichotomy is consistent with a small group, meaning it has an odd number of positive traits, it gains a +1 score and if it is inconsistent, meaning it has an even number of positive traits, it receives a -1 score. Just because it is consistent or inconsistent does not mean the dichotomy is necessarily right or wrong, because the dichotomies it is scored against may also be incorrect. At the end, all the scores will be compared to find correlations.

Inconsistent Consistent Inconsistent Inconsistent E E E E

N N N N P P P P T T T T Consistent Inconsistent Inconsistent +2 -5 = -3, likely false E E E E

N N N N P P P P T T T T

From this test, extroversion received a pretty negative score, indicating that it is likely a mistype based on the other data.

Now the remaining fourteen dichotomies must go through the same process. For each dichotomy, all seven calculations have been condensed into a single diagram.

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Intuitive Logical Irrational Farsighted +4-3 = +1 +2-5 = -3 +4-3 = +1 +3-4 = -1 E E E E

N N N N P P P P T T T T Yielding Dynamic Aristocratic Strategic +6-1 = +5 +3-4 = -1 +3-4 = -1 +2-5 = -3 E E E E

N N N N P P P P T T T T Emotivist Positivist Decisive Merry +4-3 = +1 +4-3 = -1 +6-1 = +5 +4-3 = +1 E E E E

N N N N P P P P T T T T Results Asking

+6-1 = +5 +4-3 = +1 E E

N N P P T T

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Ranked in order, the dichotomies with a green score are most consistent, the yellow scores are neutral, and the red scores are inconsistent

+5 Yielding -1 Farsighted +5 Decisive -1 Dynamic +5 Results -1 Aristocratic +1 Intuitive -1 Positivist +1 Irrational -3 Extrovert +1 Emotivist -3 Logical +1 Merry -3 Strategic +1 Asking

From this list, the three most probable errors are a mistyping of extrovert, logic and strategic. If these three dichotomies can be resolved, then the type becomes IEI with 100% confidence. Depending on how this method works in practice, it may be reasonable to assume these three dichotomies change automatically. If not, at least attention can be focused resolving the three most likely sources of errors.