Everything Unknown and Little-Known About the Eight Functions of the Psyche. Part I: Calculation of Functions, Quantitative Values of All Functions in a Psychotype, Substantive Content of Functions

V. L. Talanov

Saint Petersburg, February 2012

In December 2011, this work was conceived in the format of an article, but little by little it turned almost into a book. Division into parts and chapters became unavoidable because of the volume of material. So be it. In the end, however, it became possible to give unambiguous answers to most of the questions regularly raised in socionics concerning the eight hypothetical functions of the psyche.

This work (Part I) analyzes in detail the problem of defining the eight functions of the psyche in socionics. By combining experimental data and theoretical calculations, it is demonstrated what the numerical values of each of the eight functions of the psyche (Ni, Ne, etc.) specifically equal in each TIM. Matrices of coefficients are theoretically derived and experimentally confirmed for representing each function as a linear sum of the 16 psychotypes with weighting coefficients and, conversely, for representing each psychotype as a linear sum of the eight functions with weighting coefficients. Intercorrelation tables for psychotypes and functions are presented. A number of misconceptions concerning functions that are widespread among some socionists are analyzed. Tables of the principal psychological properties that most precisely and selectively characterize the substantive content of each of the eight functions of the psyche are presented. Experimental data indicating a relationship between socionic functions and individual characteristics of human brain physiology are partially analyzed.

Table of Contents (Part 1)

Introduction

Chapter 1. The Problem of Defining the Eight Functions of the Psyche in Socionics

Chapter 2. Obtaining Projections of a Psychological Property onto the Eight Socionic Functions from Known Projections of the Property onto the 16 Psychotypes

Chapter 3. Obtaining the Magnitudes (Values) of Functions Within a Psychotype - Depending on the Position (Program, Creative, Contact, Mobilizing, etc.) Occupied by the Function

Chapter 4. Other Approaches to Determining Function Values Within TIMs

Chapter 5. Solving the Inverse Problem - Reconstructing the Projections of a Psychological Property onto the 16 Psychotypes from Its Known Projections onto the Eight Socionic Functions

Chapter 6. Mutual Correlations of Functions.

Chapter 7. Principal (Marker, Characteristic) Properties of the Eight Socionic Functions of the Psyche That Characterize Their Substantive Content with Maximum Exclusivity

References

Introduction (on the Methods Used, Adopted Units of Measurement, and Terminology)

Experimental Basis of the Study

The material of the present work uses both purely theoretical conclusions based on mathematics and experimental results - both in cases where they could not in principle be dispensed with and in cases where it was necessary to illustrate the correctness of the theoretical derivations made. All experimental results were obtained in a study of 5,450 people using diagnostic psychological questionnaires. The questionnaires were used to identify the respondent’s dominant socionic psychotype and to construct the respondent’s complete “type profile” (that is, for all standard socionic psychotypes, a quantitative measure of the respondent’s commonality with each psychotype was calculated). The same questionnaires were used to study various psychological properties and to determine how they are related to each particular psychotype. The questionnaire methods used are described and analyzed in detail, with substantiation of their required high reliability and validity, in works [1 -17].

Use of Enlarged Clusters of Psychological Properties

More than five thousand specific questionnaire statements, collected and statistically processed over the course of a multi-year experiment and rated by respondents by “trying them on” themselves, were manually grouped by us - on the basis of their semantic content and mutual correlations - into approximately 2,300 enlarged clusters, containing from one to several dozen questionnaire items that were similar in meaning (and, in addition, mutually correlated) and that generally characterized more generalized psychological properties. On the one hand, replacing the primary questionnaire statements with their generalized clusters simplifies the presentation of the results because it reduces the number of primary properties that must be surveyed; on the other hand, averaging across several items further increases the precision of the projections of psychological properties onto psychotypes, functions, and the poles of socionic traits.

Universal Units for Measuring Arbitrary Heterogeneous Psychological Properties

In the human population, every psychological property has substantial variation in the magnitude of its expression. Sometimes its magnitude can be determined by objective methods, but in psychology expert assessments or expert self-assessments are more often used to characterize a property quantitatively (in the latter case, the respondent themself acts as the expert). Whatever units we use to measure a property (whether the deflection of a galvanometer needle or the total number of points obtained on self-rating scales in a questionnaire), its magnitude can subsequently be converted into universal units that make it possible to compare completely different properties with one another (including a person’s height with their weight, the degree of reddening of the cheeks with the speed of a muscular reaction, and so on). This becomes possible because, in the human population, the distribution of the magnitude of every property follows a quasi-Gaussian law of random distribution. The shape of this distribution on a graph is a bell-shaped curve. At the edges of the distribution, people with “extreme” values of the property are rare; their specific frequency and their proportion in the overall population are very small, whereas closer to the middle of the distribution the “crowd becomes denser.” For example, most men are between 170 and 180 cm tall, and only a comparatively small percentage of the population falls in the ranges 150-160 cm and 190-200 cm. All bell-shaped distributions are similar to one another because each has a midpoint (the population mean) and each is characterized by a width (the so-called standard deviation - its reference value is set by the condition that, when it is laid off in both directions from the population mean, 66% of all members of the population must fall into this “double band”). Thus, using the statistical language of percentages, it becomes possible to compare height and weight quantitatively, the frequency of sneezing and willingness to give one’s life for the Motherland. Whether properties are expressed in meters or kilograms, once their statistical distribution has been constructed they can be compared quantitatively with confidence. One need only determine by how many fractions of a standard deviation each of them deviates from its population mean, and in which direction. For example, one man is 175 cm tall, while another weighs 140 kg. Which is greater? A height of 175 cm lies near the middle of the population distribution of human height. Approximately equal numbers of people will lie to the left and right of this point on the graph. Perhaps this height is only slightly below average, deviating downward from the population midpoint of the height distribution by one tenth of a standard deviation. We then say that the person’s height equals “minus 0.1 standard deviation.” A weight of 140 kg, however, is already an extreme value, since only a small percentage of men in the population have an even greater weight. This point is close to the right edge of the distribution and deviates considerably from its midpoint toward the “heavyweights.” Suppose it deviates from the population midpoint by 2 standard deviations. As a result, we can now compare the first person’s height with the second person’s weight because both quantities are expressed in the same universal units. One person’s height is -0.1 standard deviation, while the other’s weight is +2 standard deviations. Clearly, in these comparable units (no longer centimeters and kilograms), the weight is greater than the height, and one can even say by how much (by 2.1 standard deviations).

Terms

Expressing arbitrary properties of interest to us in universal units - fractions of a standard deviation taken with a minus or plus sign - shows the location of the expression of each property relative to some mean. Completely different properties can then, since they are now measured in the same units, be added and subtracted, correlations between them can be calculated, and so on. Both mathematical statistics and experimental psychology, which makes intensive use of its methods, are built on this basis. In what follows, all quantities characterizing the values of various psychological properties are given by us in fractions of a standard deviation unless otherwise specified. These quantities show by how many fractions of a standard deviation the expression of a property deviates from its “socionic mean.” What is the “socionic mean”? This quantity is much more convenient for presenting results than the population mean. It is close to the population mean, but nevertheless differs from it. Suppose we have calculated the mean TIM values of some psychological property for all TIM groups (that is, for all 16 psychotypes). If we then average all 16 of these group means in turn, this will be the socionic mean. We emphasize that the socionic mean does not mean either the population mean or the sample mean. Both in the population as a whole and in a sample of respondents, different TIMs may be represented with unequal frequencies. The socionic mean does not depend on which TIMs are represented more frequently in the experimental sample and which less frequently. Its value for any property remains unchanged and independent of the particular sample on the basis of which the property was measured (which psychotypes it consisted of and in what proportions). Since, before properties are placed in the tables, the socionic mean is subtracted from their magnitude, and since the properties themselves are expressed in fractions of the universal unit - the standard deviation of the distribution - all properties in the tables ultimately turn out to be normalized relative to the socionic mean, with a mean value (with respect to the 16 psychotypes) equal to zero and a standard deviation (with respect to the interindividual dispersion of the indicator in the population) equal to one. Sometimes in the article the standard deviation is defined not by the dispersion of individual people’s indicators in the population (“population standard deviation”), but by the dispersion of this indicator among its mean values in the 16 psychotypes (“socionic standard deviation”). Such cases are also specified. The socionic standard deviation is always somewhat smaller than the population standard deviation (because the dispersion among mean type values is, for obvious reasons, always smaller than the dispersion among individual values of the same indicator for all people in the population).

All correlation coefficients discussed in this work are coefficients of linear correlation. They may be measured either over an array of many people or over an array of many psychological properties. In the first case, correlations are measured between series of two different, differently named characteristics over the same ordered set of people. In the second case, the following is meant. In the array of 2,300 psychological properties used by us, each psychotype is characterized by its own group-mean values separately for each of the 2,300 properties considered. Each such value characterizing a psychotype can also be regarded as a projection of a particular property onto the psychotype or, conversely, as a projection of the psychotype onto the property. The same is true not only for psychotypes but also for psychic functions, because each function is calculated as the mean value of the properties of several psychotypes. If the work speaks of a correlation between two psychotypes, what is meant is the coefficient of linear correlation between two series of projections (from psychotype No. 1 and psychotype No. 2) onto all the various psychological properties. The same applies to correlations between psychic functions - here too, what is meant is a correlation between two series of projections (from one function and from the other) onto the same ordered set of psychological properties.

In the present exposition, we will use the concept of a “socionic function” for all eight theoretical constructs (Ni, Ne, Si, Se, Ti, Te, Fi, Fe) introduced by Aušra Augustinavičiūtė to explain the properties of the 16 psychological types of people. We will also use the concept of a function’s position within a TIM (for the first ring of Model A - program, creative, contact, mobilizing; and for the second ring of Model A - demonstrative, controlling, activation, and suggestive). The concept of an aspect, by which socionics usually means a function occupying a particular position within a TIM, will not be used; for the purposes of this article, it appears superfluous to us and only introduces unnecessary theoretical and terminological confusion.

Chapter 1. The Problem of Defining the Eight Functions of the Psyche in Socionics

Any disputes about the substantive content of the eight socionic functions of the psyche must be preceded by a definition (specification, definition) of what we understand by functions. Otherwise, such discussions are, at best, empty talk and, at worst, finger-counting divination and anti-scientific mythmaking.

The point is that functions as the “gears” of Model A are a virtual hypothetical construct. Even if Model A were not itself a hypothetical model and reflected reality not merely at the global level of behavioral predictions, but also at the level of the brain’s immediate physiological or informational mechanisms (which is already highly doubtful), even then no one would be able to “extract” the gears from the model in order to study them directly. Only integral psychotypes are accessible to investigation, and only their properties can be reliably described (and are described) in psychological experiments. Only by proceeding from the already known properties of psychotypes can we subsequently speak about the common properties of particular groups of psychotypes. It is along this path that both our conceptions of socionic traits (extraversion-introversion, irrationality-rationality, intuition-sensing, logic-ethics, judiciousness-decisiveness, etc.) and our conceptions of the properties of functions arise (thus, to illustrate the properties of Ni in the program position, the properties of the IEI and ILI psychotypes are usually averaged, while the properties of Ni in the creative position are studied by averaging the properties of EIE and LIE). The conceptions of function signs favored by some socionists are likewise based on the properties of individual psychotypes (how adequately they correspond to experimental results is another discussion we may eventually reach).

Experiment is the head of everything. Only experiment, not a vote of authorities, is entitled to draw conclusions about which properties are characteristic of functions and which are not. But as soon as we turn to experiment, we immediately encounter its unchanging, strictly logical requirement: “You ask what the properties of functions are - and the answer can be given on the basis of the well-known properties of psychotypes; but first define the properties of precisely which combinations of psychotypes you understand as the properties of particular socionic functions of the psyche.” This is a reasonable requirement. It is unfortunate that it is sometimes forgotten (especially by those comrades who do not like becoming acquainted with experiment). At first glance, what is most often meant by the properties of functions in particular positions seems clear. But only at first glance. For example, for the program position of Ne (so-called intuition of possibilities), let us define Ne_program = mean(ILE; IEE). It must be kept in mind, however, that the same formula also serves to identify the properties of Si in its suggestive position. To identify the properties of intuition of possibilities in the creative position, the formula Ne_creative = mean(LII; EII) is used - but it must likewise be kept in mind that the properties obtained in this way will simultaneously be properties of vulnerable Se (and perhaps even more precisely its properties, the properties of a deficit of Se, than properties of the presence of creative Ne, because Ne in the creative position may not be such a large positive deviation above the mean level, whereas Se in the vulnerable position is a very large Se deficit that lowers its values far below the mean level). All the more must it be remembered that, at least for the properties of functions in the creative position, the formula of averaging two psychotypes gives a very strange result - according to it, creative Ni, judging by the properties thereby identified, turns out to be an extraverted rational function, and so on. Hence a growing doubt arises concerning the preceding formula for calculating the properties of functions in the program position as well - is everything really all right with it; can the result obtained by averaging the properties of two types with a program function truly be attributed exclusively to the properties of the program function? Thus, ambiguities arise already at the level of defining the properties of program and creative functions.

For the time being, nevertheless, let us believe these formulas. If we define the properties of all eight functions in their program and creative positions in the manner indicated above, then calculate these properties quantitatively from the known properties of the psychotypes, and then compile all these properties into tables, we can subsequently compare these properties with one another - for example, by calculating coefficients of linear correlation among all the functions (eight program and eight creative). Using 2,300 generalized psychological properties and calculating correlations among the loadings of all 16 functions on these properties, we carried out this work and obtained the following intercorrelation matrices (Tables 1.1 and 1.2).

Table 1.1. Linear correlations between function properties. Correlations were calculated over an array of 854 selected, most precisely measured properties, each calculated by averaging over from 2,620 to 66,000 points. Correlations analogous in the positional relationship of the correlated functions in each separate 8x8 subtable were replaced by their mean values (means for all possible pairs of functions with the corresponding positions in a TIM’s Model A).

Table 1.2. Linear correlations between function properties. Correlations were calculated over an array of 1,500 psychological properties with relatively low measurement precision (namely, each calculated by averaging over from 144 to 2,600 points). Correlations analogous in the relationship of the correlated functions in each separate 8x8 subtable were replaced by their mean values.

What is important for us at present in these tables is that the correlations between same-named functions in the program and creative positions are not positive at all, but negative (the value -0.08, close to zero, in the more reliable Table 1.1). This result is not at all surprising. Program Ni incorporates all the introversion and irrationality of the two psychotypes IEI and ILI from which it is calculated, whereas creative Ni, defined as we defined it above, incorporates all the extraversion and rationality of the EIE and LIE psychotypes. The commonality of the properties of Ni in the program and creative positions follows from the fact that in both cases the poles of “intuition,” “decisiveness,” and “dynamicity” are the same, whereas the difference between their properties follows from the differing poles of extraversion-introversion, irrationality-rationality, carefreeness-foresight, and tactics-strategy. The result is almost an even balance, but the differing extraversion-introversion tips the scale slightly and gives the final correlation a “minus” sign.

What, then, should we do to find the properties of Ni (or any other function) “as such,” without distinguishing its position within a TIM - program, creative, or some other position? The first thing that seems to come to mind is to completely eliminate the influence of extraversion-introversion and irrationality-rationality from the properties of functions in the program and creative positions under consideration. In fact, this will happen automatically if we simply average the properties of same-named program and creative functions. Thus, for Ni, its supposedly remaining “immanent” properties associated with its belonging to the poles of intuitives, decisives, and dynamics would then be calculated by the formula Ni = mean(IEI; ILI; EIE; LIE). But with this version of representing Ni, none of its properties associated with the function’s introversion and irrationality would enter the final table. Yet we are accustomed to considering the functions dominant in a psychotype as precisely what determines both its behavioral extraversion-introversion and its behavioral irrationality or rationality. Here, however, it would turn out that everything associated with the psychotype’s energy and its inclination toward planning (or, conversely, improvisation) is stored somewhere in the psychotype as though on its own, without being reflected in the functions, while the functions carry entirely different loadings. We would then no longer have any right, from old habit, to call Ni “introverted intuition” and Ne “extraverted intuition”; both functions would also lose the specifically shared “irrational” properties of perceiving functions, and so on and so forth. Are we prepared to accept this?

In fact, the definition of a psychic function through an algebraic sum of the 16 psychotypes (and, what is mathematically the same thing, through different loadings on socionic traits) can be specified in different ways. As we will now see, there is no complete arbitrariness here; there nevertheless exists a single optimal solution, and according to this optimal solution a single suitable formula for specifying a function is found. It turns out that the example considered above, in which a function (more precisely, its properties) is specified by averaging the four types containing the function in the first two positions, is by no means such an optimal method. To arrive at the single optimal solution for expressing any function through the 16 psychotypes taken with different weights, let us first formulate a number of initial, boundary, and auxiliary conditions for solving this problem, on which we will rely in the course of the calculations:

1. For any psychological property, the algebraic sum of the loadings on it of all 16 psychotypes is zero. By loadings we mean the projection of a psychotype onto a property or the projection of a property onto a psychotype (these are almost the same thing - if the vectors are normalized by length, any projection equals the cosine of the angle between them). The equality to zero of the algebraic sum of the values of a psychological property in all 16 psychotypes follows from the fact that this sum is proportional to the socionic mean, while the socionic mean of any property is specified by us as zero. The sum of the loadings of all eight psychic functions on any property is also identically zero. This is because a function is expressed in some way through psychotypes, and whatever this expression may be, after all eight functions are summed, each psychotype in the resulting algebraic sum of psychotypes will be repeated the same number of times, that is, with the same weight. Thus, the sum of all functions taken with equal weight will be proportional to the sum of all psychotypes, likewise taken with equal weight, that is, ultimately proportional to the socionic mean (and hence ultimately equal to zero). From this follows, in particular, the practical conclusion that the decomposition of a function into a sum of psychotypes with certain weighting coefficients is determined, at least theoretically, up to the addition of the same algebraic constant to each of these weighting coefficients. Similarly, the decomposition of a psychotype through the sum of the eight functions with certain weighting coefficients is also determined up to the addition of the same algebraic constant to all these coefficients (that is, any positive or negative number identical for all terms of the decomposition). Nevertheless, the solution for finding the weighting coefficients becomes unique if we stipulate that the algebraic sum of all weighting coefficients of the decomposition (the decomposition of a function through psychotypes or of a psychotype through functions) must equal zero. This condition is very useful because it guarantees that the results of calculating the properties of functions and types do not depend on errors in the “zeroing” of the socionic mean of psychological properties (and in practice such zeroing errors are inevitably present to some extent because calculations of the socionic mean are based on experimental data).

2. The properties of a function, when it is decomposed through an algebraic sum of psychotypes with weighting coefficients, must fully contain (reflect) the properties associated with the poles of the traits “extraverts-introverts,” “irrationals-rationals,” and “dynamics-statics” assigned to it. The properties (and hence the decomposition through psychotypes) of intuitive and sensory functions (Ni, Ne, Si, Se) must additionally reflect the properties of the poles of the traits “intuitives-sensors” and “judicious-decisive,” while the decomposition of logical and emotional functions (Ti, Te, Fi, Fe) must additionally reflect the poles of the traits “logical-ethical” and “merry-serious.” No other socionic trait should enter the immanent properties of functions - this is because all other traits, apart from those indicated, are associated not with the strength or dimensionality of the function as such, but only with the evenness or oddness of its position in TIM models or with its adjacency to other functions in these same models (as, for example, occurs in the case of the “aristocrats-democrats” trait).

3. In addition to the preceding condition No. 2, the following must be kept in mind. In solving the problem of decomposing a function into a series over the 16 psychotypes, we proceed, as it were, from the inverse problem of decomposing a psychotype into a series over the functions. We consider that, within the scope of those of its properties associated with the traits of extraversion-introversion, irrationality-rationality, statics-dynamics, intuition-sensing, logic-ethics, judiciousness-decisiveness, and merriness-seriousness, a psychotype is a linear superposition of the properties of the functions it contains. These are the properties that belong immanently to functions as such and are therefore automatically transferred into the psychotype when a linear superposition of functions is formed. Each psychotype is a superposition of the properties of all eight functions taken with certain weighting coefficients. All eight functions in this superposition possess properties of irrationality-rationality, extraversion-introversion, and statics-dynamics (each with its own sign, of course, and each making its own contribution to the psychotype through these traits). But only half of all functions (4 of 8) possess properties of the traits “intuitives-sensors,” “logical-ethical,” “judicious-decisive,” and “merry-serious” (for example, Ti does not possess properties of the “intuitives-sensors” or “judicious-decisive” traits; for these traits it is merely neutral ballast, and so on). Thus, the contribution of the latter four traits to the resulting variance of psychotype properties is diluted and halved. For these four traits to be reflected in the properties of the psychotype not in a form reduced by half, but in full, each of the four functions carrying a loading on these traits must carry it in an increased form (compensating for the “neutrality” of the other four functions). If the contribution to variance must be doubled, this means that the loading of each function on the corresponding trait must be increased by a factor of 1.414 (the square root of two, because the contribution to variance is proportional to the square of the loadings). The “square-root rule” follows from the corresponding theorems of mathematical statistics. Thus, an “ideal function” must carry a loading on the traits of extraversion-introversion, irrationality-rationality, and statics-dynamics with coefficient = 1, and on the traits “intuitives-sensors,” “logical-ethical,” “judicious-decisive,” and “merry-serious” with coefficient = 1.414. Its loading on all other traits must equal 0. Note that defining a program function as the mean value of two psychotypes having that function in the program position does not satisfy the stated condition. In a program function specified in this way, first, all loadings on the traits equal 1 (rather than 1.414 for two of the four selected traits), and second, the coefficients for carefreeness and tactics for perceiving functions and for yieldingness and constructivism for judging functions turn out to equal plus or minus 1 rather than 0, as required. Calculating a function as the mean of its program and creative positions, that is, as the mean of the properties of the four psychotypes in which the function occupies the first or second position, also fails to satisfy the stated conditions. In this case, the coefficients for tactics, constructivism, carefreeness, and yieldingness do indeed become zero, but together with them the coefficients for extraversion-introversion and irrationality-rationality are also zeroed (which is clearly unacceptable), while the coefficients for intuition-sensing, logic-ethics, and the two quadral traits (judiciousness and merriness) equal not 1.414, as required, but one - just as for the “statics-dynamics” trait.

4. It can be mathematically proved that the present fourth condition is equivalent to the preceding third condition. One is equivalent to the other; one strictly follows from the other. We will not undertake the proof of equivalence here, however, and will simply formulate the condition after first giving some necessary explanations. If we seek a representation of a psychotype through an optimal linear superposition of eight functions that preserves the maximum of the psychotype’s properties, we find this representation in the form of a matrix (see Table 5.3 in Chapter 5), where the rows correspond to the 16 psychotypes sought and the eight columns correspond to the eight functions. Each psychotype is sought and found as a weighted sum of the eight functions, with the weighting coefficients located in the cells of the matrix in the row corresponding to that psychotype. When, conversely, we seek an expression of each of the eight functions through a weighted sum of the 16 psychotypes, we use a matrix with eight rows and 16 columns, where again the weighting coefficients before the psychotypes for finding any one of the eight functions are located in the cells of the matrix row corresponding to the sought function (see Table 2.3 in Chapter 2). The fourth condition under consideration is that these two matrices are obtained from one another by mirror reflection along their diagonal - that is, when the rows of one matrix are replaced, to complete coincidence, by the columns of the other matrix, and vice versa. Such matrices are called inverted. The fourth condition states that the matrices for obtaining the weighting coefficients used to represent functions through psychotypes and the weighting coefficients used to represent psychotypes through functions must be mutually inverted. It can be mathematically proved that the requirement contained in this condition leads precisely to the weighting loadings of the traits “intuitives-sensors,” “logical-ethical,” “judicious-decisive,” and “merry-serious” being increased by a factor of the square root of two, when function values are calculated through a superposition of traits or the equivalent superposition of the 16 psychotypes, relative to the loadings of the traits of extraversion-introversion, irrationality-rationality, and statics-dynamics.

Chapter 2. Obtaining Projections of a Psychological Property onto the Eight Socionic Functions from Known Projections of the Property onto the 16 Psychotypes

Before you become completely entangled in formal mathematical conditions and circumstances, let us return to clear and sufficiently obvious tables.

Table 2.1. Required loadings of the sought psychic functions on the poles of socionic traits (up to multiplication by a constant). The loadings are presented in the columns of the table. For any traits absent from the table, their loadings for each function are taken to be identically zero.

Note that in each row of the table the sum of the squares of all loadings equals 8. This ensures that, for all seven socionic traits presented in the table, their contribution to the variance of any psychotype (when it is represented through some superposition of functions) is the same as the contribution these traits have in the original psychotype itself. If the weighting coefficients of four traits (intuition-sensing, logic-ethics, etc.) were not increased by a factor of the square root of two, this condition could not be fulfilled. Then, when a type was represented through a superposition of functions, the resulting representation of the type would underrepresent the contribution of four traits (intuition-sensing, logic-ethics, judiciousness-decisiveness, merriness-seriousness).

Table 2.2. Weighting coefficients (in the rows of the table) for representing seven socionic traits through a weighted sum of the 16 psychotypes. The value 0.063 = 1/16.

Now, to obtain the coefficients for expressing each of the eight functions through the 16 psychotypes, it is sufficient, for example, to find the coefficient corresponding to the Ni function and the ILE psychotype by taking the scalar product of the column of Table 2.1 corresponding to Ni and the column of Table 2.2 corresponding to ILE. And so on and so forth. As a result, we obtain the following Table 2.3 for finding the eight functions through the 16 psychotypes (more precisely, this table makes it possible to find the properties of each function through a superposition of the properties of the 16 psychotypes taken with specified weighting coefficients):

Table 2.3. Weighting coefficients (in the rows of the table) for the ideal representation of the eight functions of the psyche through the 16 psychotypes. According to this table, the loading of any function by any psychological property is determined as a linear weighted sum of the loadings of all 16 psychotypes by that property, with the property loadings for the psychotypes being summed after multiplication by the corresponding weighting coefficient from the rows of Table 2.3.

Now, after creating Table 2.3 (this is the most important table in the entire article), the problem of defining each of the eight functions of the psyche (“socionic functions”) has been completely and unambiguously solved. Let us consider several examples of applying Table 2.3.

Example No. 1. Let the property under consideration be pure extraversion, expressed by a magnitude equal to 1 standard deviation from the socionic mean. Then the value of this property for all 16 psychotypes (that is, the projection of extraversion = 1 onto all 16 psychotypes) is expressed by the row of Table 2.3.1.1:

Table 2.3.1.1. Example 1: loadings (projections) of unit extraversion onto the 16 psychotypes.

To find the projection of extraversion onto any psychic function (for example, Ni), that is, the loading of Ni by extraversion, one must take the scalar product of the row of Table 2.3.1.1 and the row of Table 2.3 corresponding to Ni, that is, find the sum of the products of the elements in the two rows. The result = -1, meaning that the loading of Ni by the property of unit extraversion equals minus one. The loadings of all eight functions defined according to the rules of Table 2B can be calculated and checked analogously for all 15 socionic traits. We obtain the following values:

Table 2.3.1.2. Results of checking the loading of the socionic functions, specified by the coefficients of Table 2.3, by the 15 socionic traits. Calculations according to the algorithm examined in Example No. 1. The verification results fully correspond to the values in Table 2.1 (an expected and regular result).

Example No. 2. Let the property under consideration now be some specific psychological property, for example, “laziness, relaxation, and disorganization” (which, incidentally, is closely associated with the irrational pole). The loading of the 16 psychotypes by this property (in fractions of its standard deviation) is known because it has been studied experimentally, and is presented in the row of Table 2.3.2.1:

Table 2.3.2.1. Loading of psychotypes by the property “laziness, relaxation, disorganization” (in fractions of the population standard deviation from the zero socionic mean).

Now, using Table 2.3, we will find the loading of all eight socionic functions by this property by taking the scalar product of the single row of Table 2.3.2.1 with the rows of weighting coefficients in Table 2.3 corresponding to the eight functions. As a result, we obtain the result summarized in Table 2.3.2.2:

Table 2.3.2.2. Loading of the eight socionic functions by the property “laziness, relaxation, disorganization,” calculated according to Table 2.3 (in fractions of a standard deviation from the zero socionic mean).

Example No. 3. Let the property under consideration now be the fact that the respondent belongs to the ILE psychotype. Full attention now! This is an important example with very important consequences, and here the line of reasoning must be followed carefully in order to avoid errors.

First, let us examine an incorrect line of reasoning, because much can be learned even from this example. It might seem that in a table analogous to Table 2.3.2.1 from the preceding example, this property should take the value = 1 in the column for ILE (that is, in the first cell of the row) and values equal to zero in the columns for all other psychotypes - that is, in all subsequent cells of the row (see Table 2.3.3.1). As a result, by taking the scalar product of the single row of this table with the corresponding rows of Table 2.3 (that is, by finding the sum of the pairwise products of the elements of the two rows), we obtain in Table 2.3.3.2 the projections of all eight functions onto the ILE psychotype. These would supposedly be the numerical values of each of the eight functions in this psychotype, which are of considerable interest to us.

Table 2.3.3.1. Loading of psychotypes by the property “Belonging to the ILE psychotype” (or, equivalently and more precisely, “possessing the complex of ILE traits”). This table is valid only under the erroneous assumption that all psychotypes are supposedly completely independent of one another and have no selective mutual pairwise correlations, because only then can the loadings of all psychotypes except ILE by the property “possessing the complex of ILE traits” be considered completely identical.

Table 2.3.3.2. Values of the eight socionic functions in the ILE psychotype obtained under the erroneous assumption of the preceding Table 2.3.3.1 that the psychotypes are not correlated with one another.

We see that, under the erroneous assumptions used concerning the “mutual equidistance and mutual independence of all psychotypes,” the strongest function in ILE is program Ne, followed in magnitude by creative Ti, then contact Se, while mobilizing (also vulnerable) Fi is the weakest. Moreover, differentiated values are obtained only for the static functions of the first ring. All functions of the dynamic pole included in the second ring of Model A are undifferentiated in magnitude in ILE (= -0.07) and evidently have a “shadow” character. The same numerical values for the functions as in Table 2.3.3.2 are also obtained under the assumption that the psychotypes are correlated with one another, but only through equal contributions to the variance of properties from all seven socionic traits entering the functions. What is meant is that exactly the same numerical result is obtained if one assumes that the influence of differences in the poles of extraversion on type properties (and ultimately on the variance of these properties) is the same as the influence of differences in the poles of statics-dynamics, and so on. In this case, for example, ILE turns out to be positively correlated with the properties of LII, SLE, and IEE (because ILE shares more than half of the socionic trait poles with them), while with ILI and LIE the correlation of ILE would be not positive but weakly negative - equal to the same correlation with LSE and SLI (most trait poles are different between ILE and all these types). But from experience we know that ILE clearly has more properties in common with LIE than with LSE; likewise, more common properties will be found between ILE and ILI than between ILE and SLI. This is because the contributions of different socionic traits to the total variance of psychological properties are by no means equal. For example, the contribution of extraversion-introversion or logic-ethics is far greater than the contribution of substantive differences in properties determined by the trait “merry-serious,” and so on. Therefore, the assumption of equal contributions of the seven socionic traits to the variance of psychological properties is obviously incorrect. Indeed, the contribution of extraversion and of traits associated with the balance of intuition-sensing and logic-ethics to most substantial psychological properties is clearly greater than, for example, that of merriness-seriousness or statics-dynamics.

Thus, the results of Table 2.3.3.2 contradict the truth because they proceed either from the assumption of equal contributions of the seven socionic traits to the total variance of psychological properties or, still more strongly, from the incorrect assumption either of the complete independence of the 16 psychotypes from one another or at least of their mutual equidistance in the multidimensional psychological space of properties, that is, supposedly of the absence in their pairs of any preferential mutual correlations between their properties. But if such selective correlations of properties between psychotypes exist (and they do), and if the influence of extraversion on psychological properties is stronger than that of the “merry-serious” trait (and so on), then we have no right whatsoever to put zeros in 15 cells of Table 2.3.2.1. In all these cells we must place the real, empirically found coefficients of correlation between the properties of the 15 corresponding psychotypes and the properties of the ILE psychotype of interest to us (or numbers proportional to them) - because these, not rashly inserted zeros, are the real loadings of all psychotypes differing from ILE by the properties of ILE. Yes, the first cell will indeed contain one (the linear correlation of a psychotype with itself equals one; this is indisputable), but all the other cells will contain not zeros at all but very different numbers, namely the correlations of the properties of the corresponding psychotypes with the properties of ILE, and their values can be learned only from experiment.

Fortunately, we possess such experimental data.

Chapter 3. Obtaining the Magnitudes (Values) of Functions Within a Psychotype - Depending on the Position (Program, Creative, Contact, Mobilizing, etc.) Occupied by the Function

In the experimental sample of 5,440 respondents whose psychotypes had been determined with high precision using diagnostic questionnaires (on average, with reliability no worse than 90%), we selected a subsample consisting of 240 men (15 people of each of the 16 types) and 640 women (40 people of each of the 16 types). In all members of the subsample, psychotypes were diagnosed with especially high reliability (above 95%). Recall that questionnaires diagnose psychotypes by the method of correlations between the respondent’s answer vector and 16 reference vectors representing previously obtained averaged answers of representatives of each TIM to the same questionnaire questions. The result is the so-called personal experimental TIM profile of each successive new respondent, consisting of 16 empirically found coefficients of linear correlation. The highest correlation in this profile (and the more contrastively it is expressed, the better and more reliable the conclusions) corresponds to the respondent’s sought psychotype. Thus, our subsample consists of 880 TIM profiles (each expressed by 16 correlation coefficients with reference TIMs). The respondent’s TIM is determined by the largest correlation coefficient, but the remaining 15 cells in each TIM-profile row are not empty or zero - some contain positive numbers, others negative ones. For each psychotype (separately for groups of 15 men and 40 women), an average TIM profile can be determined. It turns out that the TIM profiles of men and women are, for each TIM, in good agreement with one another (the mean coefficient of linear correlation between the “male” and “female” profiles across all 16 TIM profiles is 0.98). The resulting profiles can then be normalized (by multiplying all elements of a row by the same number so that the standard deviation of the coefficients in the row equals 1.00). The male and female profiles can then be averaged with one another and, finally, analogous coefficients in the rows of each of the resulting average TIM profiles can be averaged. For example, in the row for ILE we obtained a loading of ILE itself = 2.34 and of LIE (a type differing from ILE in irrationality-rationality) = 1.32. In the row for LII we obtain a loading of LII itself = 2.07 and of ILI (a type differing in irrationality-rationality) = 1.37. We then average 2.34 with 2.07 and with 14 analogous coefficients from the other TIM profiles, and 1.32 with 1.37 and with 14 analogous coefficients from the other TIM profiles, and so on. As a result, for the final averaged TIM profiles, which equally reflect all psychotypes and equally reflect men and women, we obtain the following Table 3.1:

Table 3.1. Standard TIM profiles for all 16 psychotypes obtained by analyzing a subsample of 880 people (each profile is located in a row, consists of 16 numbers, and reflects the weighted loadings of all 16 different psychotypes by the properties of the “heading” psychotype of the row, marked in yellow).

Why the diagonal elements of the matrix in Table 3.1 are maximal (=2.22) is clear. Each psychotype among the matrix columns is, naturally, maximally loaded by its own properties. But the other cells are not empty either - in each row, the elements are proportional (with an amplification coefficient = 2.22) to the correlations that the properties of the psychotypes named in the column headings have with the properties of the psychotype named in the row heading. In the first row, the deepest negative coefficient is found for ESI - this too is understandable. Compared with ILE, ESI has the opposite polarity for extraversion-introversion, irrationality-rationality, logic-ethics, and intuition-sensing. Only the socionic trait statics-dynamics, which is reflected only very weakly in questionnaire items and therefore in the psychological properties actually being compared, has the same polarity in these psychotypes. The second-largest positive coefficient in the first row, however, is found for LIE (=1.28), which coincides with ILE in extraversion-introversion, logic, and intuition, but differs in irrationality-rationality, judiciousness-decisiveness, merriness-seriousness, and statics-dynamics. Three trait poles coincide (among those important for socionic functions), while four differ. If all traits had equal influence on psychological properties, we would have a negative coefficient for LIE in the first row, that is, in the profile decomposing ILE into loadings of all 16 psychotypes. But the influence of extraversion-introversion, logic, and intuition on real psychological properties (and hence on those used in diagnostic questionnaires) is several times greater than the influence of irrationality-rationality, statics-dynamics, and so on. This is why the correlation between the properties of ILE and LIE is positive and high, and why the coefficient for LIE in the first row of Table 3.1 is positive and quite large in magnitude (the largest). ILE has many properties in common with LIE - far more than with ESI or SEI. Thus, all coefficients in each row are proportional to the real correlations, found in practice, between the properties of the type named in the column and the properties of the type named in the row. Correlations between the properties of different psychotypes depend on the different weighted effects that different socionic traits, in total and overall, exert on psychological properties. If extraversion-introversion contributes twice as strongly to people’s psychological diversity as irrationality-rationality, one system of coefficients will result for Table 3.1. If, conversely, irrationality-rationality were to contribute twice as strongly and weightily to people’s psychological diversity as extraversion-introversion, Table 3.1 would contain a completely different system of coefficients.

We have now obtained for the ILE TIM profile a completely different row of coefficients from the simplified and coarsened one previously presented in Table 2.3.3.1. We can now use the coefficients of the previously obtained Table 2.3 to transform the first row of Table 3.1, representing the loadings of the 16 psychotypes by the properties of the ILE psychotype, into loadings of the eight socionic functions by the properties of the ILE psychotype. These loadings will simultaneously be the values of the eight functions in the standard average ILE TIM - this is easy to verify (see Chapter 5) if the psychotype profile is reconstructed from the function profile using an inverted matrix (inverted Table 2.3, where rows and columns exchange places). This inverse operation almost completely reconstructs all the original TIM profiles of Table 3.1, except for the small error (and the correspondingly very small percentage of properties, less than 6%) caused by the traits not encoded in functions: “democrats-aristocrats,” “questims-declatims,” “process-result,” “positivists-negativists,” “constructivists-emotivists,” “tacticians-strategists,” “yielding-obstinate,” and “carefree-foresight.” Although there are, at first glance, many of these traits that are fundamentally not encoded in the functions, no more than 6% of the total variance of a TIM’s psychological properties is associated with them (in practice, even less than 6%).

Thus, by applying the matrix of Table 2.3 to the TIM profiles of Table 3.1, taking as the function loading the scalar product of the row of the theoretically derived Table 2.3 for the function of interest and the row of the experimentally obtained Table 3.1 for the TIM of interest, we finally obtain a table of the values of the socionic functions in all “standard” psychotypes - see Table 3.2:

Table 3.2. Averaged function values for the 16 averaged “standard” psychotypes (equal-weight averaging of questionnaire results from 15x16=240 men and 40x16=640 women).

Table 3.2 shows that the functions of the first ring in “averaged” representatives of each psychotype take the following values:

program = +1.63 - that is, its value lies 1.63 standard deviations above the socionic mean (taken as the zero reference level; here the standard deviation is measured by the dispersion of the function magnitude among all 16 psychotypes, and it approximately corresponds to the standard deviation of the population dispersion of the function magnitude, although, generally speaking, it is somewhat smaller);

creative = +0.03 (practically no different from the socionic mean level, which is close to the population mean);

contact = -0.04 (practically the same in magnitude as the creative function - therefore, in some accentuated representatives of TIMs it can even exceed the magnitude of the creative function);

mobilizing (also “vulnerable”) = -1.48 (the lowest value among all eight functions of a TIM);

For the functions of the second ring, the descending hierarchy of function values begins with the function in the demonstrative position:

demonstrative = +0.90;

controlling = +0.37;

activation = -0.38;

suggestive = -1.02.

Many people, on seeing these results, will immediately experience an instinctive protest. What is this? Ti in ILE is weaker than Te! In LII, Ni is stronger than Ne! How can that be? It turns out that in the properties of its logic, ILE resembles LIE more than LII. But are we not accustomed to seeking (and easily finding) in the properties of ILE’s logic primarily the static, structural, Ti component that makes it akin to LII? Yes, we seek and find it because, in doing so, we diligently try to identify and discern only the specific static-dynamic component of logic mixed with the common judicious quadral values that indeed make ILE and LII akin, while just as diligently closing our eyes to the energetic (extraversion-introversion) component and so forth. Comparing ILE and LII, as it seems to us, “by their logic,” we are in reality comparing these two types only by their statics and by their genuinely common quadral values, and naturally, with such an approach, find more in common than when comparing ILE with LIE. Unfortunately, with such an approach we are feeding on illusions. Trying to discern the properties of logic, we unconsciously, under the influence of a corresponding initially false psychological set, substitute the common quadral and static-dynamic properties of the types for logic. If we cool our bias, we will soon see that ILI is quite capable of systematizing structural-logical work (almost like LII - its Ti is also greater than Te), whereas the “standard” ILE is noticeably less capable of such work (its Ti is less than Te). Analogously, in ethics IEE will have noticeably more in common with EIE and ESE than with ESI and EII; but in ethical observation and a certain ethical masochism mixed with compassion (characteristic features of Fi), IEE is inferior to IEI, in which, unlike in the “standard” IEE, Fi > Fe (even though this is expressed far less contrastively than in EII, the tendency is the same). And so on and so forth.

We again remind the reader that all function values in their particular positions within a TIM are given above in fractions of the standard deviation of the socionic distribution of the function magnitude, while the sign of the value indicates deviation of the function magnitude upward or downward from the socionic mean value taken as conditional zero (that is, the mean value obtained by averaging across all 16 “standard” psychotypes). We see that the first-ring functions have the widest range in magnitude (from +1.63 for the program function to -1.48 for the mobilizing function). The range of magnitudes of the second-ring functions is smaller - from +0.90 for the demonstrative to -1.02 for the suggestive.

We emphasize immediately that the cited function values depending on their positions within a TIM are only averages for all representatives of the same TIM. In individual people, depending on their accentuation, deviations in the values of particular functions upward or downward will necessarily be observed. These changes in magnitude can even be large enough to alter the formal hierarchy of function magnitudes within a ring. For example, the creative function may be weakened and the contact function strengthened, changing their order of magnitude (but not, however, changing the selective character of the “pairing” of the program and creative functions). Within an accentuation, the creative function may, conversely, be strengthened. Accentuation of first-ring functions usually also affects the magnitudes of second-ring functions. As an example, we will present the average functional profile of people who choose scientific research activity as their most preferred profession. If you think that the requirements of scientific research work are optimally satisfied by “pure” LII or ILE types, or by both together, you are greatly mistaken. Our study of the functional profiles of three dozen people who confidently chose science as a profession, and especially the study of the profiles of several people successful in science, showed that what is optimal for science is not “pure” but “mixed,” accentuated profiles that correspond to no pure type. Here is the portrait of this profile of socionic functions that is ideal for most sciences (at least the natural sciences):

This table shows that a scientist needs strong Ti, Ni, and Ne. Excessively strong Ti, however, characteristic of the “standard” LII, is more likely to hinder a scientist (because it turns them into a pedant). Fe is of no value, while Te at the population-average level is sufficient. Intuition, however, must be strengthened relative to the ordinary LII level, and not only Ne but Ni as well. Ne in a good scientist should be above average, but Ni should be especially well developed and should be at the same level as Ti (or even slightly higher). Yet in socionics there is a myth that scientific success depends only on Ne, not on Ni. This is not so. Why? Ne makes it possible to grasp analogies quickly, but strong Ne interferes with concentration on a goal, promotes a “jump of ideas,” and promotes superficial thinking detached both from systematization (Ti) and from the criteria of practice together with its requirements of the “beauty of harmony” (Si). Si is also responsible for spatial representations, memory, and the desire to touch and share, without which science is not science. Unlike very weak Si, which hinders the scientist through its weakness, very weak Se does not hinder a scientist but helps (the less Se, the greater the shift toward the “judicious” pole with its respect for the individual and simultaneously altruistic respect for universal human interests - and the need for altruistic motivation in doing science is by no means the least important matter). Ni is required at a high level because it provides orientation toward the future and the past, as well as sequential, sometimes cyclic comparison, through cyclic reminiscences, of points in time with one another, that is, orientation toward past experience (the ability to rummage through memory is an indispensably important trait for an experimenter). Ni also provides the leisurely “contemplative” quality needed by a scientist - simultaneously freedom from worldly bustle, attentiveness to what is happening around one with only the unusual singled out, and the ability “not to twitch,” to precede every step with numerous mental experiments. Through its criticality and perpetual dissatisfaction, Ni also provides exactingness (including toward one’s own fantasies), another trait necessary to a scientist. It is no accident that among the many male ILEs examined by us within one experimental project, not one (in contrast to a good ten LII and about five ILI) expressed a desire to engage in scientific research. Those historically known ILEs who nevertheless left a significant mark on the history of science must, one may suppose, have had very strong introverted accentuation - in the form of strengthened Ti and Ni accompanied by weakened Ne. But even in such cases, people of the ILE type most often enter the history of science through “flashes” of one or two bright ideas that had almost no influence on contemporaries during their lifetime but were appreciated by descendants many years later - and even then most often for reasons of national priority. Such was the fate of both Tsiolkovsky and Vernadsky. Modern science is all the more not carried out by flashes of brilliant ideas but by long experiment; it is made along the path of numerous trials and errors. Here the profile of a “pure” ILE is entirely unsuitable. Even for a science-fiction writer, an excess of static Ne is not good - writing requires that very same Ni to a much greater extent. What, then, prevents ILI from being a scientist? In general, nothing. It is only necessary to raise Ti higher and weaken Ni (for LII the opposite applies). A “Balzac” engaged in science is likewise necessarily an accentuated “Balzac,” with strengthened rational-evaluative Ti and weakened Ni. Moreover, “Balzacs,” even when accentuated in the required way, are nevertheless rarer guests in science than appropriately accentuated “Robespierres,” because greater Ni and relatively greater Se shift them, unlike “Robespierres,” toward the “decisive” pole. The values of this pole tend toward egoism; willingness to work for an idea and on enthusiasm is rare here, as is the motivation to bring benefit to all humanity (“to discover in order to share with everyone”). These motivational matters are also a most important part of successful scientific work. Thus, in any case, pure types are unsuitable for science; it requires accentuations - and invariably finds them, most often in “analysts” with strengthened irrational functions, less often in somewhat more egoistic, passive, slow, and minor-key “critics” by virtue of their program function (Charles Darwin), but likewise accentuated in the direction of strengthening evaluative, systematizing, and system-forming Ti. Note that the only LSI who also showed interest in pure science as a profession in our study had, as an accentuation, a substantial strengthening of Ni up to positive values and a reduced magnitude of program Ti. Se was also reduced relative to the type norm, while Ne was slightly increased, which in combination provided relative softness of his “decisive” traits.

Writing likewise requires accentuated types, not pure types - judging by the results of our study of people’s professional preferences, the optimal profile for it is closest to standard IEI, but accentuated toward a substantial strengthening of Ne with Ti additionally raised up to population-average values - all accompanied by a reduction in Si (we think that the writer Viktor Pelevin has precisely such a profile). Fortunately, there are plenty of accentuated types in nature, which is why there are also many good writers.

One more remark concerning Table 3.2, to which we have already partly drawn the reader’s attention above. The issue is important and deserves repetition. It is customary, for example, to consider Te in the ILI psychotype to be higher than in the LII psychotype. The table shows that this is not so and that the statement is only a myth. In “average” representatives of a rational psychotype, both leading rational functions, program and controlling, turn out to be greater in magnitude than the same rational functions in a quasi-identical psychotype differing in irrationality-rationality. In the average LII, controlling Te = 0.37, while in the average ILI, creative Te = 0.03, that is, only slightly but nevertheless smaller in magnitude (and in addition, it is smaller than demonstrative Ti in the same average ILI). Apparently, the conception of exceptionally “businesslike” ILIs and science-immersed ILEs and LIIs arises in the public consciousness of socionists mainly from those representatives of these types whose creative function is accentuated and strengthened (an example of a strongly expressed creative ILI is Elena Baturina, wife of Y. Luzhkov). Ordinary LIIs, without creative accentuation, are rarely scientists and more often merely Ti pedants. Likewise, ordinary ILIs are by no means quick, entrepreneurial Te heroes, but more often merely inert and lazy contemplative skeptics who, thanks to developed controlling Ne, have high creativity (higher than the average LII) and who only because of this, together with their impulsive irrationality and the greater egoism and lesser respect for other people’s property caused by Ni-related “decisiveness,” sometimes appear more entrepreneurial. In terms of Te itself, rather than complex entrepreneurial abilities related to it only very indirectly, average ILIs are slow to get moving and are not especially calculatingly greedy or purposeful with respect to profit (the average “analyst” will be greedier and more calculating than the “critic” - Te is stronger, and less creative - Ne and Ni are weaker, but at the same time much less prepared for the harsh rules of business because of greater decency - the balance of decisive and judicious functions is shifted toward judiciousness). Business is more “decisiveness” than Te. The difference between LII and ILI in favor of slightly higher Te in LII becomes even more obvious and understandable if one considers that the most characteristic marker trait of Te is perhaps not so much calculation as self-confident imperturbability, self-confidence. No prejudiced judgments about TIM properties have yet formed in socionics on this subject, so this example probably makes it easier to see the sometimes stronger Te in the average LII when comparing it with an equally ordinary and typical ILI. Analogously, the Ne creativity of ILI is slightly higher than that of LII, while Si concentration and love of experiencing new sensations are higher in SEE than in ESE, and so on. Deviations from this rule are observed, as already stated, only with initial accentuations, that is, with additional strengthening of creative functions. For example, impulsive aggressiveness (in particular, liking to fight) is higher in the average SLI than in LSI. But for creative subtypes of LSI and SLI, aggressiveness will already be noticeably higher in LSI.

Chapter 4. Other Approaches to Determining Function Values Within TIMs

As shown in the preceding Chapter 3, the basic information for determining function values within a TIM is the availability of a somehow determined row of loadings of that TIM on all 16 TIMs of the socion. This can be obtained only from experiment. In essence, this row shows in its 16 cells the commonality of the TIM under consideration with each of the other TIMs. The degree of commonality in each case depends on which socionic traits are more heavily weighted for us in considering this commonality and which are less heavily weighted. For example, if commonality in extraversion-introversion is more heavily weighted than commonality in statics-dynamics, the row for ILE will show higher coefficients of commonality between this TIM and other extraverted TIMs and a weaker commonality with other static TIMs. Which socionic traits are more heavily weighted in filling the functions with information, and which are less heavily weighted (this is ultimately precisely what is at issue), can of course be specified “out of thin air,” but our approach in the preceding chapter was to take this information from life, from experiment, which shows the degree of influence of different socionic traits on the sum of the psychological properties used to diagnose psychotypes. This approach will remain unchanged in the present chapter, but here we will attempt to change something else.

In the preceding chapter, to construct the rows of commonality of each psychotype with the other TIMs (its loadings on all the other TIMs), we selected from the experimental sample 880 people with TIM profiles determined in the experiment (each of which represents correlations between the respondent’s questionnaire answers and the averaged “reference answers” of the 16 “standard” psychotypes), divided these 880 people into 16 psychotypes, and simply averaged the already available (experimentally measured) TIM profiles of the respondents for each psychotype. Now we will proceed differently. We will measure correlations between individual TIM loadings over the array of all 880 respondents. Again we obtain a 16x16 matrix (similar to Table 3.1), in which each row (for example, the first, for ILE) contains the correlation of our respondents’ loadings on this ILE type with their loadings on all the other psychotypes. As we can see, with this approach there is no need at all to divide respondents into groups with different psychotypes, that is, to diagnose their psychotype in advance. The same can be done not for the subsample of 880 respondents in which psychotypes were deliberately represented with equal frequency, but for the full sample of 5,400 respondents (for whom profiles of commonality between their answers and the 16 references had likewise been determined). For this case, for example, we obtain the intercorrelation matrix of the type loadings of these respondents shown as an example in Table 4.1:

Table 4.1. Intercorrelation matrix of type loadings in the primary type profiles of 5,400 respondents to psychological questionnaires.

Next, once again using the matrix of Table 2.3 in relation to the TIM profiles of Table 4.1 (or any other table showing the relationship of each psychotype to other psychotypes), and taking as the function value the scalar product (that is, the sum of pairwise products of elements with the same ordinal number) of the row of Table 2.3 for the function of interest and the row of Table 4.1 (or a similar table) for the TIM of interest, we once again obtain a table of socionic function values for each of the 16 psychotypes. It may also be necessary to normalize the resulting rows of function values in psychotypes so that the dispersion of the magnitudes of the eight functions in each psychotype corresponds to one standard deviation. What ultimately results for the magnitudes of the eight functions within all TIMs depends on which matrix of intertype relationships (of the Table 4.1 kind) we use.

The intercorrelation matrix of type loadings (like Table 4.1) can be obtained in different ways, and not necessarily over an array of respondents. It can also be constructed over an array of psychological properties for which their type profiles are known (showing how frequently a given property is manifested in representatives of each type). Then, over the array of all properties (for example, the array of 2,300 generalized psychological properties used in our studies), another intercorrelation matrix of intertype correlations can be calculated. This method too will ultimately lead us to its own table of function values within TIMs. What results from the different calculation methods is shown in Tables 4.2-4.4.

Table 4.2. Function values within TIMs corresponding to the intercorrelation matrix of pairwise commonalities of the 16 TIMs calculated over an array of primary diagnostic correlations in a subsample of 880 people.

Table 4.3. Function values within TIMs corresponding to the intercorrelation matrix of pairwise commonalities of the 16 TIMs calculated over an array of primary diagnostic correlations in the full sample of 5,400 people.

Table 4.4. Function values within TIMs corresponding to the intercorrelation matrix of pairwise commonalities of the 16 TIMs calculated over an array of known type loadings of 1,000 generalized psychological properties with the most precisely determined type loadings.

Comparing the results of Tables 3.2, 4.2, 4.3, and 4.4, it is easy to see that the results for function values within TIMs based on different approaches to determining pairwise commonalities among TIMs do not differ all that greatly. For clarity, we will combine the results from the first rows of all these tables (for functions in the ILE TIM) into a single Table 4.5:

Table 4.5. Comparison of function values within the ILE TIM obtained on the basis of different approaches to estimating pairwise commonalities between psychotypes.

In conclusion to this chapter, let us again draw attention to the fact that, by all calculation methods, the magnitude of the function in the demonstrative position (Te in the case of ILE) turns out to be substantially greater than the magnitude of the creative function (Ti in the case of ILE; see Table 4.5). It is important for the reader to understand why this happens. If we consider that a TIM’s extraversion-introversion properties are and should be reflected in its eight socionic functions (or “psychic functions” - we will not dwell on terminology that differs among authors), then the result of Table 4.5 for ILE, where Te > Ti, is natural. To ensure the extraversion of the ILE type as a whole after the contributions of all eight of its functions are added together, it turns out to be inevitable that extraverted logic Te must have a greater value in the ILE TIM than introverted logic Ti. If, however, we do not wish to associate functions with extraversion-introversion loadings (but in that case we lose the right to call functions extraverted or introverted), if, accordingly, we wish to strip any extraversion-introversion properties completely out of the substantive content of functions, then we must make changes to Table 2.1 and subsequently to Table 2.3, by means of which the functions are calculated (in the form presented, this table proceeds from the assumption that a function must reflect and contain extraversion-introversion, irrationality-rationality, and statics-dynamics properties, and moreover in the same proportional shares in which they appear in any TIMs). As long as we do not abandon the rule that every function must reflect extraversion-introversion, irrationality-rationality, and static-dynamic properties of the psyche in exactly the same proportional shares in which they appear in integral TIMs, we should not be surprised that a function in the demonstrative position turns out to be substantially greater in magnitude than a function in the creative position, nor should we be surprised by the other “unexpected” features of Tables 3.2 and 4.2-4.4.

Chapter 5. Solving the Inverse Problem - Reconstructing the Projections of a Psychological Property onto the 16 Psychotypes from Its Known Projections onto the Eight Socionic Functions

First, let us remember that socionic functions do not reflect all socionic traits, but only some of them - albeit the most substantial ones. Therefore, it is impossible in principle to reconstruct from the functions, however they are combined with one another, all the complete information about a psychotype. To understand what share of information we can reconstruct, let us consider Table 5.1 for illustration.

Table 5.1. Calculation of the percentage contribution of socionic traits to the total variance of psychological properties associated with those traits. The cells indicate percentages of the total variance of properties associated with the given socionic trait or, in the final rows, with groups of socionic traits. The calculation was performed separately for three different cases.

Table 5.1 shows that, by any calculation, from 93% to 97% of the total variance of all kinds of psychological properties is associated with the immanent properties of the eight socionic functions. This part of the properties is determined only by the weighted contribution of particular socionic functions to the psychotype and is in no way associated with their position within the psychotype, much less with their adjacency to other socionic functions within the psychotype. No more than 3% of the total variance is associated with peculiarities of the functions’ positions within the psychotype (for example, whether a function is program or creative, rather than with the magnitude of the function itself), while certainly less than 4.5% of the total variance of psychological properties is associated with adjacency of functions (which functions are immediate neighbors within a TIM), with the lion’s share of these percentages attributable to the “aristocrats-democrats” trait. As a “lyrical digression,” let us draw the readers’ attention to how little variance in an array of the most varied psychological properties turns out to be associated with the so-called “weak” socionic traits - they are called weak for good reason. From this you can draw your own conclusion about how unreliable type diagnosis is when based on “weak” socionic traits (questimity-declatimity, positivism-negativism, etc.).

Thus, the overwhelming share of the variance of psychological properties (93% or even more) is associated with the individual weighted content of all eight functions of the psyche in the psychotype, and with nothing else. What matters here is only the “strength” or “power” of each function, or, if you prefer, its “dimensionality” - that is, something characterized by a numerical value of its magnitude - and it does not matter at all which position the function occupies within the psychotype or which other functions it borders and interacts with. All this 93% of property variance is easily modeled, evidently, by a linear additive superposition of the eight functions with weighting coefficients. It is precisely this 93% of the information from the total psychological information contained in the properties of the original psychotype that is reflected in the eight psychological functions; and subsequently, from these functions, knowing their individual weighted contribution to each psychotype, all information about the psychotype properties associated with the functions can be reconstructed. It follows that the maximum attainable coefficient of linear correlation between the properties of the original psychotype and the properties of the psychotype reconstructed from the eight functions (by representing each psychotype as a linear superposition of eight functions with particular weighting coefficients before each of them) equals the square root of 0.9246 = 0.96 (because, according to the theorems of mathematical statistics, the coefficient of linear correlation between two properties equals the square root of the share constituted by the common variance of these properties in their complete total variance). If the contribution of traits Nos. 1-7 to the total variance of properties is taken to equal 97.16% (the case in which the weighted contribution of traits is calculated over an array of primary diagnostic correlations with type references in the subsample of 880 respondents), then the correlation between psychotype properties “reconstructed” from functions and their original properties reaches the square root of 0.9716 = 0.986. Anticipating what follows, we will say at once that this is exactly what is obtained when the correlations between the properties of the “original” psychotypes and the psychotypes reconstructed from functions are checked experimentally.

The problem of reconstructing psychotype values from the values of the eight functions consists in seeking the optimal combination of weighting coefficients in the formula for a linear superposition of functions that would provide the maximum coefficient of correlation between the properties of the original psychotypes and the properties of psychotypes reconstructed through the superposition of functions. The superposition approximating an arbitrary psychotype is sought in the form:

S = a1*F_program + a2*F_creative + a3*F_contact + a4*F_mobilizing + a5*F_suggestive + a6*F_activation + a7*F_controlling + a8*F_demonstrative

The system of sought coefficients from a1 to a8 is the same for all psychotypes and is tied not to the names of the functions but to their roles, that is, their positions within a TIM. Thus, the magnitude of the coefficient before a function depends only on what that function is for the TIM: program, creative, contact, mobilizing, suggestive, activation, controlling, or demonstrative. Let us recall, using Model A for the ILE TIM as an example, which specific positions of functions within a TIM these names correspond to:

The conditions we impose on the search for the system of coefficients a1-a8 are as follows. First, a1+a2+a3+a4+a5+a6+a7+a8 = 0 (this condition is not mandatory, but it is convenient for solving practical problems based on this system of coefficients because it frees the result from dependence on inaccuracies and errors in calculating the socionic mean; in addition, this condition makes the sought solution unique). Second and finally, the system of coefficients a1-a8 must maximize the coefficient of correlation between the projections of the original psychotypes and the projections of the psychotypes reconstructed by the superposition formula onto all 2,300 psychological properties considered by us. At the same time, the sum of squared differences between the corresponding families of projections must also be minimized. These conditions give a unique solution for finding the system of coefficients a1-a8. They can be found without any analytical or mathematical tricks, merely using the convenient “Solver” option in the EXCEL spreadsheet program, which finds the required system of coefficients by trial selection and successive approximations. The result is the following unique solution:

Table 5.2. Coefficients found for the functions (unique solution) for optimal modeling of a psychotype through a linear superposition of its eight functions (program, creative, contact, etc.).

Table 5.2 can be rewritten in a form more convenient for practical application by indicating the required coefficients for each psychotype and each named function in that psychotype (Ne, Ni, Te, Ti, etc.). This produces Table 5.3:

Table 5.3. Coefficients for optimal modeling of psychotype properties through a linear superposition of the eight socionic functions, taken with coefficients specific to each psychotype.

If all the coefficients in Table 5.3 are divided by 2, it becomes obvious that all its elements then exactly coincide with the elements of the matrix in Table 2.3, which we used in Chapter 2 to represent every socionic function (Ni, Ne, etc.) as a superposition of the 16 psychotypes with weighting coefficients (the matrices of Tables 2.3 and 5.3 coincide if one of them is flipped around its diagonal, that is, if rows are replaced by columns and vice versa). This is not surprising - the result of Table 5.3 could also have been reached purely analytically, using theorems of matrix analysis (without resorting to semi-empirical selection of coefficients), and it could have been shown purely analytically that all its rows simply must be the columns of the matrix from Table 2.3, but additionally multiplied by a coefficient = 2. The doubling of all elements of Table 5.3 relative to Table 2.3 is due simply to the fact that Table 2.3 had 16 columns, while the matrix of Table 5.3 has eight columns, that is, there are half as many superposition terms in the decomposition of psychotypes through functions as there are in the decomposition of functions through psychotypes, which is why the previous coefficients must be multiplied by 2.

Chapter 6. Mutual Correlations of Functions.

Table 2.3 gave us the ability to calculate the projection of an arbitrary property onto any socionic function if we know the projections of this property onto all 16 psychotypes. Table 3.2 (and, in addition to it, the analogous Tables 4.2-4.4) gave us the ability to know the values of socionic functions in each psychotype. If we are dealing not with pure psychotypes but with mixed, accentuated ones (that is, with real people), it is likewise not difficult to determine the value of each of the eight socionic functions in a particular person: one need only transform that particular person’s individual type profile (that is, the correlation of their personal individual psychological properties with each of the 16 standard psychotypes) into their individual functional profile - according to the same rules and procedures we used to obtain Table 3.2. That is, to obtain the value of a particular function in a given person, one must calculate the scalar product of the person’s individual type profile and the row of Table 2.3 corresponding to the function of interest.

Thus, we know everything about functions and can calculate their values both for specific people (with known type profiles), for averaged psychotypes of groups of people (each psychotype, both “pure” and accentuated, is characterized by a type profile, that is, by the commonality of the properties of this psychotype with all 16 “standard” types), and for any psychological properties (for which their type profile has likewise been measured or calculated). It remains to determine how the functions correlate with one another.

Table 6.1. Mutual correlations of functions formally calculated between the columns of Table 3.2 (correlations are calculated between series consisting of only 16 variables each, with the variables being the mean values of a particular function in each of the 16 “standard” averaged psychotypes).

Table 6.2. Mutual correlations of functions calculated over an array of 880 people between series of their personal function values.

Table 6.3. Mutual correlations of functions calculated between the functional loadings of 1,000 generalized psychological properties with the most precisely and reliably determined type and functional profiles.

As we can see by comparing Tables 6.1-6.3, the results in all cases do not differ very substantially from one another. A function correlates most strongly (from +0.31 to +0.35) with the same-named function of the opposite extraversion-introversion. Why? Because among the three socionic traits that strongly influence psychological properties (extraversion-introversion, irrationality-rationality, and the functional pole of logic-ethics or intuition-sensing), these functions (for example, the pair Ni and Ne) have the same poles of irrationality-rationality and the functional pole, while the poles of extraversion-introversion differ. This is two against one, so the correlation is positive. A positive correlation, although smaller, is observed in the pairs Ni-Ti and Ni-Fi. In these pairs of functions, their extraversion-introversion coincides, but irrationality-rationality is opposite, while with respect to the functional pole these functions are neutral relative to each other. This yields one against one, but extraversion-introversion influences psychological properties more strongly than irrationality-rationality (see Table 5.1), so the resulting correlation is positive. The deepest negative correlation is between mutually complementary functions, for example Ni and Se. The reason is that these functions have opposite extraversion-introversion and opposite functional poles, while only irrationality-rationality, comparatively weak in its influence on psychological properties, coincides. And so on. The deepest negative correlation precisely between negative functions is entirely natural from a biological point of view - this is why dual types are attracted to one another in marriage: their program functions, in terms of the genes underlying them, are maximally distant from one another and maximally opposite in genetic material. The principal conclusion from examining Tables 6.1-6.3 is that the functions are not completely independent of one another. Because each of them has an extraversion-introversion component, an irrationality-rationality component, and a specifically functional component characterizing the nature of the function (plus weaker static-dynamic and quadral components), the overlap of these components causes the functions to display mutual, selective correlational relationships.

Chapter 7. Principal (Marker, Characteristic) Properties of the Eight Socionic Functions of the Psyche That Characterize Their Substantive Content with Maximum Exclusivity

In the present chapter we will give, as examples, only a few properties of the eight functions of the psyche considered in socionics. The properties of all functions will be discussed in much greater detail in subsequent articles in the series, which will be specifically devoted to a much more detailed separate examination of groups of intuitive, sensory, logical, and emotional (ethical) functions, as well as to analysis of the biological nature of all eight functions (which proteins, neurotransmitters, genes, and brain regions underlie them). For this reason, in this chapter we present the tables of the principal characteristic (marker) properties of the functions for the time being almost without discussion.

The coefficient of correlation between the type profile of a particular psychological property and the type profile of a function (see the type profiles of functions in Table 2.3) was used to identify marker properties. Properties were selected as characteristic of a function when the corresponding coefficient of linear correlation between the type profiles of the property and the function was, first, maximal specifically for that function and, second, sufficiently large (approaching one in value). The absolute magnitude of the projection of the property onto the function was also taken into account (the point is that the type profile of a psychological property may be exclusively characteristic of a particular function, and the coefficient of correlation between the type profiles of the property and the function may approach one, while the type profile of the property itself may at the same time be smoothed, insufficiently contrastive, and “spread” across TIMs - to exclude such cases from the marker properties, the final selection criterion was taken to be the product of the correlation coefficient between the property and function profiles and the absolute value of the projection of the property onto the function).

Table 7.1. Principal characteristic properties and manifestations of the socionic function Ni (“white,” “dynamic” intuition).

In our opinion, the results obtained for the marker properties of Ni deserve a brief comment more than those for any other function. Table 7.1 shows that good ability to integrate and compare different points in time, the ability to sense or foresee the near future (especially when it involves foreseeing trouble), and a good sense of physical time (as though a clock were built in) - all these potentials are indeed, among all functions, most closely and positively associated with Ni. However, first, a number of these properties (for example, interest in the future and the ability to compare and integrate different points in time in thought activity) turn out to be consequences of a deficit of Si rather than of the presence of developed Ni, while interest in the future is, moreover, associated just as strongly or even more strongly with strong Te, not only with strong Ni. Second (and most importantly), it is not the listed abilities to operate with temporal parameters that are generally most characteristic of Ni. Its primary markers are rather the following properties:

• Tendency toward states of thoughtless contemplation, weakness of vital desires, apathy and abulia;

• Difficulty initiating movements in their initial phase, tendency toward stuporous states;

• Depressiveness, tendency toward feelings of frustration, predisposition to first discern the unpleasant and negative side in everything (the tendency toward hypochondria and biliousness toward other people characteristic of Ni are also particular manifestations of this trait);

• Predisposition to feelings of derealization and depersonalization, as well as predisposition to perceptual (visual and auditory, especially auditory) illusions and pseudohallucinations.

Let us briefly note that all the listed marker traits (together with abilities to operate with time) are usually regarded in neurophysiology as manifestations of enhanced function of the right-hemisphere anterior (including frontal) cortical regions against a background of functional weakening of symmetrically located left-hemisphere regions.

Table 7.2. Principal characteristic properties and manifestations of the socionic function Ne (“black,” “static” intuition).