Socion Archive

Monograph

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Yu.P. Minaev — Elements of Mathematical Socionics

2021

UDC 159.923+51-77

Minaev Yu.P. Elements of Mathematical Socionics. — Kyiv: International Institute of Socionics, 2021. — 158 pp.

Reviewers: A.V. Bukalov, PhD in Psychology, PhD in Socionics; G.R. Reinin, PhD in Psychology, PhD in Socionics

The monograph the author offers to the reader’s attention contains material that until now could only be found in articles from the journals published by the International Institute of Socionics. A new instrument of socionic infographics, named the “Socionic Compass,” was recently proposed, which has made it possible to present in compact form the results obtained in recent years in the field of mathematical socionics.

The foundations of an original “symbolic calculus” laid down by the author of the monograph have made it possible to substantially simplify the procedures for deriving consequences from the premises embedded in socionic models. The system of formalized notation developed for the operators of intertype relations and for the bipolar traits of types of information metabolism makes it easy to carry out the necessary “calculations” without resorting to cumbersome tables or socionic calculators.

The monograph can be used by students studying socionics as a textbook for reaching, relatively quickly, a level that allows them to think critically when reading the socionics literature.

© Minaev Yu.P., 2021 © International Institute of Socionics, 2021

Table of Contents

  • Preface — 5
  • Chapter 1. What the Socionic Compass Shows — 9
    • From Jung’s Compass to the Socionic Compass — 9
    • A System of Formalized Notation for the Operators of the Classical Intertype Relations — 14
    • Partitioning the Socion by Means of the Proper Subgroups of the Group of Operators of the Classical IR — 28
    • The Socionic Compass as a Basis for Constructing Two 16-Element Groups of Bipolar Traits of TIMs with a Common 8-Element Subgroup — 36
    • The Socionic Compass and the Models “A” of the TIMs — 53
    • Conclusion to Chapter 1 — 60
    • References for Chapter 1 — 61
  • Chapter 2. Operators of Intertype Relations as Operators of Transformations of the Models “A” of Types of Information Metabolism — 63
    • The Group of Operators of the Classical IR as a Group of Operators of Transformations of the 2D Models “A” of TIMs — 63
    • The Group of Operators of the Classical IR as a Group of Operators of Transformations of the 3D Models “A” of TIMs — 72
    • The Group of Operators of the Classical IR as a Group of Operators of Transformations of the One-Dimensional Models “A” — 83
    • The Two Languages of Thinking in Vekker’s Theory and the Rules for Combining Functions of Information Metabolism into the Blocks of Model “A” — 92
    • Conclusion to Chapter 2 — 104
    • References for Chapter 2 — 106
  • Chapter 3. A Look at the Bipolar Traits of Types of Information Metabolism from the Standpoint of the Classical Intertype Relations — 108
    • Generating “New” Groups of Central Sections of the Socion on the Basis of “Old” Bipolar Traits of TIMs — 108
    • Dichotomies of the Socion into Halves Homogeneous from the Standpoint of the Classical IR, and “Single-Formula” Tetrachotomies of the Socion with the Superego Operator in the “Formula” — 117
    • “Single-Formula” Tetrachotomies of the Socion without the Superego Operator in the “Formula” — 122
    • “Single-Formula” Octochotomies of the Socion into Homogeneous Pairs of TIMs — 128
    • Conclusion to Chapter 3 — 132
    • References for Chapter 3 — 134
  • Chapter 4. Classical Orbital Tetrachotomies and Verbalized Dichotomies of the Socion — 135
    • History of the Question and Formulation of the Research Problem — 135
    • The 217 Orbital Tetrachotomies of the Socion — 138
    • The 15 Factorization Tetrachotomies of the Socion — 139
    • The 114 “Two-Formula” Orbital Tetrachotomies of the Socion — 145

(remaining TOC entries follow in the next installment once verified against the body text)

Preface

I first came across the phrase “mathematical socionics” in one of the books by S.I. Churyumov, PhD in Psychology. The chapter bearing that title opened with an analysis of the contribution made to this field by G.R. Reinin, PhD in Psychology and PhD in Socionics. By the time Semyon Ivanovich’s book came out, I was already acquainted with two of Grigory Romanovich’s books and had even written my first articles, which were published in the “Mathematical Methods in Socionics” section of the journal Socionics, Mentology and Personality Psychology.

Those articles were directly connected with the material of the books by Grigory Romanovich and by Semyon Ivanovich himself. It so happened that in my articles I was, on the one hand, supporting and developing the ideas of these two well-known socionists, while on the other hand I often found myself in the role of their critic.

I am grateful to Semyon Ivanovich for a decade of quite active scholarly communication, which prompted me to reflect on improving the mathematical apparatus of socionics and to write articles on the subject.

For the past several years I have had the opportunity to communicate with Grigory Romanovich Reinin using modern means of communication. Over the course of our exchanges we have published four joint articles of considerable length, written in the form of dialogues between us. At first we discussed his books and my quibbles with them, and later we examined the results obtained by me and my students.

I wish to express my gratitude to Olga Bogdanovna Karpenko, who not only made her own contribution to the development of mathematical socionics but also encouraged my work in this direction. In particular, she drew my attention to articles by other authors on the subject.

An interesting experience for me was the joint work with Andrew Joynton, an upper-year student at the University of Colorado Colorado Springs and administrator of the Socionics Math group (Facebook). Having become acquainted with some of my works, he contacted me on his own initiative. Three of our joint articles have already been published. Andrew Joynton took a liking to the system of formalized notation I had proposed for the operators of intertype relations and for the bipolar traits of types of information metabolism. Using this notation, he created a whole series of remarkable illustrations that can be drawn upon when presenting the mathematical apparatus of socionics.

Inspiring for me was the interaction with my younger colleagues, who took an active part in the discussions and in preparing articles for publication. In roughly half of all my articles on socionics the co-author is I.P. Datsenko (Keneva), whom I have known since the days when she was still studying at a physics-and-mathematics lyceum. It was she — by then already a student of the physics faculty of Zaporizhzhia National University — who drew my attention to the socionics literature.

I think that not only I but my younger colleagues too are glad of our acquaintance with I.Yu. Litvinenko, PhD in Socionics, who lives in our city (Zaporizhzhia) and is always ready to give a talk before us and take part in discussing our work.

The proposal to summarize the results of our research in mathematical socionics by writing a monograph came two years ago from the director of the International Institute of Socionics, A.V. Bukalov, PhD in Psychology and PhD in Socionics. For that external push I am very grateful to Aleksandr Valentinovich.

Since there was a great deal of my own material, and it was so unfamiliar to many experienced socionists — to say nothing of beginners — it was decided to forgo a survey of others’ work and to concentrate on explaining my own approaches to developing the mathematical apparatus of socionics. I wanted this monograph to be able to serve also as a textbook for my students at Zaporizhzhia National University.

For several years running I taught the course “Foundations of the Theory of Types of Information Metabolism” to master’s students in the specialty “Secondary Education (Physics).” But starting this academic year it has been replaced by a new course, “Person-Oriented Physics Teaching.” And although socionics could well have served as the scientific basis of such teaching, in this course the emphasis will shift toward the particular didactics of a specific school subject. The classroom time devoted to the mathematical apparatus of socionics proper will therefore, of course, be reduced. Students will need a textbook to help them master the necessary material in a more independent mode.

Students who have felt from their own experience how knowledge of the mathematical apparatus of physics helps in mastering the factual material of physics do not need much convincing that knowledge of the mathematical apparatus of socionics will help them in mastering socionic knowledge. And the hope that socionics will also help them in their future profession, and in life generally, arises in many of them rather quickly.

The structure of the monograph is such that serious work on the text of the first chapter will enable students to master those “elements” of the mathematical apparatus of socionics with which they will already be able, fairly quickly and in their heads, to carry out the necessary operations without resorting to cumbersome tables or socionic calculators.

In that chapter they will become acquainted with a recently devised instrument named the “Socionic Compass,” whose prototype was the well-known “Jung’s Compass.” This new instrument makes it possible to grasp a whole range of ideas of mathematical socionics and to learn to obtain, independently, concrete results that follow from the workings of socionic models. Admittedly, the first chapter contains no justification of why the abbreviated symbolic notations of the types of information metabolism can, in many problems, replace the Models “A” of the types of information metabolism that socionists are accustomed to.

The second chapter is in the main devoted to an extended explanation of why, in constructing and studying the group of operators of the classical intertype relations, one may pass from it to the easily surveyable group, isomorphic to it, of operators of transformations of the symbolic notations of the types. The passage to the so-called symbolic calculus of intertype relations spares students from having to study the far more cumbersome and not particularly convenient formalism of matrices and substitutions that was proposed in the early stages of the development of mathematical socionics.

The third chapter is entitled “A Look at the Bipolar Traits of Types of Information Metabolism from the Standpoint of the Classical Intertype Relations.” For those who have read G.R. Reinin’s books, this title should call to mind his “Analysis of Intertype Relations from the Position of the Group of Bipolar Traits.” This chapter examines in detail the procedure of partitioning the socion by means of the proper subgroups of the group of operators of the classical IR. With this approach to partitioning the socion it becomes obvious that, from the standpoint of the classical IR, the bipolar traits of TIMs do not look equal in standing. Moreover, from this standpoint it turns out to make sense to pay attention to yet another group of bipolar traits, one that shares a common 8-element subgroup with the Augustinavichiute–Reinin group of traits.

The fourth chapter demonstrates how the problem of the so-called orbital tetrachotomies of the socion was solved with the help of the new methods. This is material for those prepared to immerse themselves more deeply in mathematical socionics. I will note only that Aleksey Safronyuk, who at the time was still a schoolboy, took an active part in solving this problem.

Each chapter is provided with its own list of references. At the end of the monograph there is a general “Index of Illustrative Materials.”

September 2021 — Yuri Minaev

Translator’s note: as with the SMiPL article PDFs, the information-aspect glyphs (the black/white aspect symbols) are absent from this PDF’s text layer — the source shows blank gaps where they appear, e.g. in the ЛСЭ ego-block example. They will be restored from the page images or from context (usually inferable from the surrounding type names) chapter by chapter.

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