A Comparative Analysis of Variants of Ordering the Set of Socionic Types
Yu. P. Minaev Socionics, Mentology and Personality Psychology, No. 4, 2014, pp. 5–15 UDC 159.923.2 (Section: Research)
Abstract
The question of the “strict ordering of the set of types in the socion,” posed by S. I. Churyumov, is considered. A comparative analysis of several ordering variants encountered in the socionics literature is carried out. A method is indicated for obtaining an ordered sequence of the types of information metabolism based on the Jung basis. This variant, the most acceptable on didactic grounds, satisfies the main formal requirements imposed on an ordered list of socionic types.
Keywords: socionics, “Theorem on the strict ordering of the set of types in the socion,” “Churyumov Square,” Augustinavichiute–Liashkiavichius intertype relations table, Jung basis.
Translator’s note: IR abbreviations follow the same key as before (ТО identity, СЭ super-ego, РО kindred, ДЕ business, ПО extinguishment, ДУ duality, МИ mirage, ПД semi-duality, ЗЕ mirror, КФ conflict, Р±/З± supervision/benefit, КВ quasi-identity, АК activation). Figures typeset as images did not fully survive extraction; bracketed descriptions are supplied where the prose determines their content.
Is there a problem?
It would seem that the question of the order of TIMs in the socion was settled long ago. It is fixed by V. Liashkiavichius in the “Table of Intertype Relations,” on the handwritten variant of which the founder of socionics, A. Augustinavichiute, left her autograph. This document, historic for socionics, was reproduced by G. A. Shulman in his book [12, p. 226]. On the last page of every issue of the journals of the International Institute of Socionics one can likewise see this canonized order of the socionic types. In Grigory Alexandrovich’s book it is noted that “the letter-digit quadral indexing of TIMs after N. N. Medvedev (α1–α4, β1–β4, etc.) proves very convenient” [12, p. 232].
If one turns to the characterizations of TIMs written by A. Augustinavichiute [1], at the beginning of each description one finds the corresponding designation “after Medvedev.” But looking into the book of Nikolai Nikolaevich himself, published relatively recently by the Chornaya Belka publishing house, we notice that in his table “Socionic intertype interrelations” a different order of TIMs is used: the dual pair ЛИЭ–ЭСИ (LIE–ESI) comes before the pair СЭЭ–ИЛИ (SEE–ILI) [4, p. 104]. Under the same cover as N. N. Medvedev’s “Psychological Essays” are placed very extensive commentaries on them written by V. D. Ermak. And he has his own order in the list of TIMs. Indeed, not just one.
In the figure with depictions of the models of the TIMs [4, p. 228] Vladimir Davidovich kept the order of the dual pairs the same as in Liashkiavichius’s table, but in the third and fourth quadras the introverts moved into first place in each dual pair. Immediately after the figure comes a list of “names and pseudonyms of the TIMs.” There, however, the set of TIMs is ordered quite differently. About the only things left unchanged are the order of the quadras, and the dual pair ИЛЭ–СЭИ (ILE–SEI), which kept its place in the overall list and its internal sequence [4, p. 229].
Perhaps the order does not matter? After all, G. R. Reinin too uses one ordering of TIMs in one place of his book [9, p. 155] and another in another place [9, p. 168], and neither of them coincides with that of I. N. Kalinauskas [2, p. 71], whom he cites and whose “helm” he uses. Note that Igor Nikolaevich’s order is the same as N. N. Medvedev’s.
If the sequence of TIMs within the quadras cannot be strictly determined, it would still make sense to choose it uniformly, so as not to confuse readers of the socionics literature. Of course, considerations are needed as to which sequence is preferable. Thus, one of the orders used by G. R. Reinin is connected with the “socionic cube,” which can be useful in teaching socionics [9, p. 31], while another (from Liashkiavichius’s table) can be connected with the functional roles of the TIMs in the quadra and the socion after Bukalov [7, p. 448]. But S. I. Nebykova also writes about “quadral roles” [8, p. 21], justifying “her” order of TIMs. In her case the roles in the quadra are tied to a tetratomy of the socion by means of the bipolar traits extraversion/introversion and intuition/sensorics.
Interestingly, in fact (by composition of TIMs) the same roles in the quadra also appear in S. I. Churyumov [11, p. 395]. For the Leading, Guarding, Interacting and Perceiving of Svetlana Ivanovna are the very same (after S. V. Savchenko) Kings, Queens, Knights and Pages, respectively, that came out for Semyon Ivanovich. The word “came out” is used here deliberately. S. I. Churyumov holds that he has mathematically substantiated the strict ordering of the set of TIMs, and that the fact that the columns of his table of the “Periodic System of the Types of Information Metabolism” (PSTIM) contain TIMs corresponding to the same court cards (after Savchenko) or the same stimuli to activity (after Gulenko) is additional confirmation of the correctness of his theoretical derivations.
Let us quote from Semyon Ivanovich’s book: “Aushra brilliantly indicated (an intuitive extravert!) the periodization of the types by quadras, and although she did not call them periods (which, of course, is not obligatory), in essence they are such. The only thing that needs changing in her order, contained in V. Liashkiavichius’s table, is that in the last quadra the diads of Stirlitz and Huxley should be interchanged, which follows from the structure of the Churyumov square” [11, p. 387]. However, if one takes the trouble to compare Churyumov’s sequence with that of Augustinavichiute–Liashkiavichius, a discrepancy is found in the third quadra as well. There too the diads are interchanged. To all appearances, Semyon Ivanovich was writing about one sequence but had another in mind (the one found in Medvedev and Kalinauskas). Nevertheless, the assertion that a “Theorem on the strict ordering of the set of types in the socion” has been proved must be examined.
Brief explanations of the notation used in what follows
Since I shall use notation already known from the socionics literature published for a broad readership, I shall dwell on it only briefly. The numbering of the TIMs in the 4×4 table and in the pattern of the “Churyumov Square” will be assumed as shown in Fig. 1.
Fig. 1. The adopted order of numbering of TIMs in the 4×4 table and in the pattern of the “Churyumov Square.”
[4×4 table numbered row-wise 1–16; the Square pattern numbered clockwise around the perimeter: 1 2 3 4 down the top, 5–8 down the right side, 9–12 along the bottom (right to left), 13–16 up the left side.]
Fig. 2 gives the 4×4 table with the same order of TIMs as in V. Liashkiavichius’s “Table of Intertype Relations.” In the cell allotted to a given TIM its various designations are indicated. Among them are also the designations introduced by S. I. Churyumov, in which a capital letter denotes an extraverted informational aspect (IA) and a small letter an introverted one. Semyon Ivanovich holds that they compare favorably, in speed of writing, with recording the EGO block in socionic symbols. It seems to me, however, that in this case, compared with the symbolic record, one loses such an important trait of the IA as external/internal, to which A. Augustinavichiute drew attention when explaining the introduction of the symbolism [1, p. 14].
Fig. 2. The TIM designations used.
| ИЛЭ (ILE) — Il, + | СЭИ (SEI) — sE, + | ЭСЭ (ESE) — Es, – | ЛИИ (LII) — lI, – |
| ЭИЭ (EIE) — Ei, + | ЛСИ (LSI) — lS, + | СЛЭ (SLE) — Sl, – | ИЭИ (IEI) — iE, – |
| СЭЭ (SEE) — Se, + | ИЛИ (ILI) — iL, + | ЛИЭ (LIE) — Li, – | ЭСИ (ESI) — eS, – |
| ЛСЭ (LSE) — Ls, + | ЭИИ (EII) — eI, + | ИЭЭ (IEE) — iE, – | СЛИ (SLI) — sL, – |
One more designation of a TIM amounts to depicting the symbol of the IA processed by the 1st FIM (function of information metabolism), with a ”+” or ”–” sign depending on the pole of the trait right/left. A reminder of how, from the IA of the first FIM and the sign, one learns which IA is processed by the second FIM is given in Fig. 3.
Fig. 3. The rule for determining the IA of the 2nd FIM from the aspect of the 1st FIM and the sign. [Diagram pairing intuition ↔ logic and ethics ↔ sensorics partners according to the sign.]
A simple principle allowing the set of TIMs to be ordered using the Jung basis
My attempt to find in S. I. Churyumov’s books a proof of the “Theorem on the strict ordering of the set of types in the socion” that could be accepted as mathematical was not crowned with success. Nor did the semantic arguments seem more convincing than those of other authors who use other variants of ordering the list of TIMs. This aroused the desire to construct a counterexample that would pass the check against the formal requirements of which Semyon Ivanovich writes in his works. At the same time I wanted the ordering principle to be simple enough, and the result not to provoke obvious rejection on semantic grounds.
I shall now describe a principle by means of which even a beginner in socionics can reconstruct the proposed “new variant” of the TIM list, after which the “comparative analysis” promised in the article’s title will be carried out with several other variants existing in the socionics literature. In this analysis I shall deliberately use the very tools that S. I. Churyumov developed to argue for his variant (or rather, to “prove” the absence of other possibilities).
In all the compared variants the quadral order will not be violated, and the first diad will consist of ИЛЭ (ILE) and СЭИ (SEI), in that sequence. To obtain the ordered list of types we shall be guided by the following principle, supplementing the restrictions already mentioned: in the 4×4 table, neighboring TIMs (both in rows and in columns) must have exactly one coincidence of poles of the traits of the Jung basis.
Then it is clear that after СЭИ must come ЛИИ (LII) (coincidence of poles in the trait extraversion/introversion and difference in all the rest), and after ЛИИ — ЭСЭ (ESE) (both rationals, while the remaining Jungian traits differ). And that is the whole α-quadra. Note that among the intraquadral intertype relations, the dual ones correspond to preservation of the pole of rationality, and the mirror ones to preservation of the pole of version (extra/introversion).
And who will be the column neighbors of the named TIMs? For all the TIMs of the next row to come from the β-quadra, only the poles of the trait logic/ethics must coincide. Then the order there will be: ЛСИ, ЭИЭ, СЛЭ, ИЭИ (LSI, EIE, SLE, IEI). It also satisfies the requirement on row neighbors. The third quadra comes out as: СЭЭ, ИЛИ, ЭСИ, ЛИЭ (SEE, ILI, ESI, LIE). From the three-letter codes it is clearly seen that with the column neighbors (from the preceding quadra) coincidence of poles occurs only for the trait sensorics/intuition, and in the row everything is likewise in order. The last four will have the order: ЭИИ, ЛСЭ, ИЭЭ, СЛИ (EII, LSE, IEE, SLI). The link with the neighbors from the preceding quadra in the columns is maintained through preservation of the pole of the dichotomy logic/ethics. And that is the whole ordered list of the socion (Fig. 4). Simple, is it not?
Fig. 4. The “new variant” of ordering the set of TIMs, based on the dichotomies of the Jung basis. Coincidence of poles of exactly one dichotomy is denoted: P/J — irrationality/rationality, E/I — extraversion/introversion, T/F — logic/ethics, N/S — intuition/sensorics.
ILE —P/J— SEI —E/I— LII —P/J— ESE
|T/F |T/F |T/F |T/F
LSI —P/J— EIE —E/I— SLE —P/J— IEI
|N/S |N/S |N/S |N/S
SEE —P/J— ILI —E/I— ESI —P/J— LIE
|T/F |T/F |T/F |T/F
EII —P/J— LSE —E/I— IEE —P/J— SLI
In the graphical representation of the obtained result, the known designations of the Jung dichotomies are used. Preservation of only the pole of logic/ethics out of the whole Jung basis is denoted in the scheme as T/F, and preservation of only the pole of intuition/sensorics as N/S. Coincidence only in rationality we shall denote P/J, and exclusively in version — E/I. Let us note once again that what is at issue is the coincidence or non-coincidence of the poles of only the four dichotomies forming the Jung basis. The “new variant” of ordering the set of TIMs is presented in Fig. 4 as a 4×4 table with the “links” to row and column neighbors indicated.
Representation of intertype relations in the pattern of the “Ch” square
S. I. Churyumov writes in his book [10, p. 193] that in his lecture course on socionics in 1987 he proposed a “square configuration of the socion,” in which he placed the quadras along the sides of a square. The introduction of this configuration, in his words, made it possible not only to refine the order of TIMs directly, but also to visualize internal features of the socion. In particular, it became clear that cyclic processes are possible in the socion. A quotation from the same page: “Such a model vividly demonstrates the internal symmetry of the socion. In it, opposite one another are placed TIMs standing in the relation of complete opposition, which is quite natural (emphasis mine — Yu.M.) from the point of view of symmetry, and it is natural that an uncoordinated displacement of one or several elements will immediately lead to a violation of this symmetry.” The question arises: if TIMs standing in the relation of quasi-identity were placed opposite one another, would that be less natural?
Further: “In the quadras, placed one on each side, the duals are placed side by side according to the scheme aabb (adjacent placement). The activators are placed according to the scheme abab (alternation), and the mirror partners according to the scheme abba (enclosing).” Question: if the words activators and mirror partners in this phrase are interchanged, does the probative force of the assertion decrease?
On the next page of his book Semyon Ivanovich, having given as an example the schemes of three relations, invites anyone who wishes to construct schemes for all the other relations, but warns: “Not for all relations does such symmetry result, which is quite natural, since some of the relations are asymmetric.” The author himself, as was said, gave only three figures with schemes of relations: super-EGO, conflict and supervision (“control”). The first two schemes coincided with themselves under rotation by any angle that is a multiple of 90°. The scheme for supervision did not possess this property. As should be clear from the quotation given, Semyon Ivanovich attributed this to the asymmetry of the latter intertype relation.
Let us not be lazy, and let us plot in the pattern of the “Churyumov Square” the mirage and kindred relations, which are considered symmetric. For comparison we shall do the same after changing the order of TIMs from Churyumov’s to the “new variant” (Figs. 5, 6), which was obtained in the preceding section of this article by means of the simple principle based on the Jung basis.
Fig. 5. Mirage relations in the pattern of the “Ch” square: a) order of TIMs after Churyumov; b) the “new variant”.
[In (a), the chords joining mirage partners criss-cross without rotational regularity; in (b) they form a pattern carried into itself by 90° rotation.]
Fig. 6. Kindred relations in the pattern of the “Ch” square: a) order of TIMs after Churyumov; b) the “new variant”.
[Same contrast: (a) irregular chords; (b) a 90°-rotation-symmetric pattern.]
What do we see? Unlike the super-EGO and conflict relations, whose schemes Semyon Ivanovich gave in his book, the other relations that are symmetric per Augustinavichiute may, with his order of TIMs, yield schemes not as symmetric as one would wish. For from schemes of this kind one ought to demand symmetry under rotation by 90°. That would mean that the quadra can be considered a period (as S. I. Churyumov indeed proposes). The “new variant,” on the other hand, withstands this check.
Note that some other variants of TIM placement would also “pass” this check — in particular, that of Augustinavichiute–Liashkiavichius. But with some, as with S. I. Churyumov’s variant, problems would arise. Fig. 7 gives the schemes for the mirage, kindred and complete opposition relations in the case of the ordering of the socion encountered in the books of N. N. Medvedev [4] and I. N. Kalinauskas [2].
Fig. 7. Schemes of relations in the case of the Medvedev ordering of TIMs: a) mirage; b) kindred; c) complete opposition.
[In (a) and (b) the chords lack 90° symmetry; in (c) the chords are the parallel verticals joining each TIM to the one directly opposite.]
Since, to all appearances, S. I. Churyumov arrived at his variant of ordering the set of TIMs by starting precisely from what is presented in Fig. 7, one may agree that his order has a more attractive scheme for the relation of complete opposition (his scheme would coincide with itself under rotation by 90°, for the corresponding TIMs in his placement stand opposite one another). As for such relations as the mirage and kindred ones, no particular advantage is visible.
It is convenient to compare the various variants of ordering the set of TIMs by marking the IRs between neighbors around the “Ch” square. What is meant here, of course, is not the sequence of TIMs after Churyumov, but the very idea of their ring placement. Fig. 8 presents 6 ordering variants.
Fig. 8. Intertype relations between neighboring TIMs in their ring placement for various ordering variants.
[Six rings labelled Medvedev, Churyumov, Ermak, Liashkiavichius, Reinin, and “New variant.” Within each quadra-side the neighbor relations run ДУ, ЗЕ, ДУ; the corner (inter-quadra) relations distinguish the variants: Medvedev — ПД on some corners but Р–/Р+ on others; Churyumov — corners include Р–, ПД, МИ, Р+; Ermak — corners РО and ПД mixed; Liashkiavichius — all four corners ПД; Reinin — all four corners РО; New variant — sides run ДУ, АК, ДУ with all four corners ПД.]
As is seen from the figure, in the first four variants (in all except the “new” one and G. R. Reinin’s) the order of TIMs in the first two quadras is the same. Note that of these four variants, only in the Augustinavichiute–Liashkiavichius order is a quadral periodicity of the intertype relations discernible — and the distinct relations number only three: dual (ДУ), mirror (ЗЕ) and semi-dual (ПД). All the other IRs can be expressed through them if the notion of a product of relation operators is properly introduced on the set of IRs (see, e.g., [6]). Then the set of IR operators with the introduced multiplication operation forms a noncommutative group (in the mathematical sense), and the operators ДУ, ЗЕ, ПД can be regarded as generators of this group (if you like — a basis).
It is useful to compare this result with the one obtained by O. B. Karpenko in article [3]. Olga Bogdanovna considers the group of Reinin traits and the group of IRs per Reinin. These groups have not three but four generators (a four-element basis), and the groups themselves are commutative (abelian). The distinguishing feature of the group of IRs per Augustinavichiute is that asymmetric elements appear in it, the group itself is not abelian, and three generators suffice to obtain all the elements of the group. If to the two generators (ДУ, ЗЕ) of the intraquadral group of IRs, consisting of four relations (ТО, ДУ, ЗЕ, АК), one adds ПД, this will be sufficient to obtain all the remaining IRs per Augustinavichiute present in the socion.
Let us note the fact that those IRs per Augustinavichiute which occur in a half of the socion consisting of adjacent quadras do not form a group. Indeed, there one can find the following IRs: ТО, ДУ, ЗЕ, АК, З+, З–, Р+, Р–, РО, ПД, ДЕ, МИ. It is easily noticed that (З+)² = (З–)² = (Р+)² = (Р–)² = СЭ. That is, we have a new IR, and using it we obtain the rest: ДУ·СЭ = ПО, ЗЕ·СЭ = КФ, АК·СЭ = КВ.
A different picture obtains in the group of Reinin spectrum-relations (IRs per Reinin). It has 8-element subgroups consisting of the element-relations in the octaves formed by adjacent quadras: {ТО, ДУ, ЗЕ, АК, Iз, Iк, μ, ξ} — the case of uniting non-kindred quadras into an octave; {ТО, ДУ, ЗЕ, АК, Rз, Rк, τ, ω} — the case of kindred quadras. As for uniting orthogonal quadras into an octave, the IRs occurring there are the same both in Augustinavichiute’s theory and in Reinin’s. They form the 8-element commutative (abelian) group {ТО, ДУ, ЗЕ, АК, СЭ, ПО, КФ, КВ} with a three-element basis (for example, ДУ, ЗЕ, СЭ).
Let us return to Fig. 8. In the remaining two variants (G. Reinin’s and the “new” one) there are changes in the TIM sequences not only in the last two quadras. But in these two variants as well, as in the Augustinavichiute–Liashkiavichius variant, the schemes of intertype relations reproduce themselves under rotation by any angle that is a multiple of 90°, and this testifies to the quadral periodicity of the IRs.
In the last two variants it is also clearly seen that the group of IRs per Augustinavichiute has only three, not four, generators. In the scheme of G. Reinin’s variant it is seen that the system of generators can be the triple ДУ, ЗЕ, РО, and in the scheme of the “new” variant — ДУ, АК, ПД. Note that in both variants, unlike the Augustinavichiute–Liashkiavichius order, first places in the aristocratic quadras are occupied by TIMs that are not only rational but introverted. This accords better with the idea of the introversion of the aristocratic quadras [7, p. 433].
Other “proofs” of the orderedness of the socion
As an argument in favor of his variant of ordering the set of TIMs, S. I. Churyumov presents a table in which, for each type, the poles of the Augustinavichiute–Reinin traits are marked. But the order of the ARTs is chosen not with the traditional division into individual, dyadic and quadral, but in a special way, so that the “body” of the table, filled with pluses and minuses, could be reconstructed by a simple rule [11, p. 379].
This rule turned out so simple that it could be written down in a compact formula. Such a formula representation of this rule was proposed by me in article [5]. However, in that same article it was pointed out that such a table in itself, with a structure convenient for “folding-unfolding,” is not a proof of the exclusivity of the TIM order used by Semyon Ivanovich in his works. It merely coordinates the sequence of TIMs and the sequence of ARTs with each other. I also indicated how one can obtain a table with the same “body” but with other, mutually coordinated, lists of TIMs and ARTs. Let us illustrate this by means of the “new variant” proposed in the present article (Table 1).
Table 1. The Augustinavichiute–Reinin traits with the Churyumov sign arrangement, for the “new variant” of the TIM sequence.
Trait columns (numbered 0–15): 0 — the K–Ch (Karpenko–Churyumov) existence trait; 1 — static/dynamic; 2 — right/left; 3 — positivist/negativist; 4 — democrat/aristocrat; 5 — questim/declatim; 6 — irrational/rational; 7 — extravert/introvert; 8 — merry/serious; 9 — logician/ethicist; 10 — carefree/farsighted; 11 — tactician/strategist; 12 — judicious/decisive; 13 — intuitive/sensoric; 14 — yielding/obstinate; 15 — constructivist/emotivist.
| TIM | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ILE | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + |
| SEI | + | – | + | – | + | – | + | – | + | – | + | – | + | – | + | – |
| LII | + | + | – | – | + | + | – | – | + | + | – | – | + | + | – | – |
| ESE | + | – | – | + | + | – | – | + | + | – | – | + | + | – | – | + |
| LSI | + | + | + | + | – | – | – | – | + | + | + | + | – | – | – | – |
| EIE | + | – | + | – | – | + | – | + | + | – | + | – | – | + | – | + |
| SLE | + | + | – | – | – | – | + | + | + | + | – | – | – | – | + | + |
| IEI | + | – | – | + | – | + | + | – | + | – | – | + | – | + | + | – |
| SEE | + | + | + | + | + | + | + | + | – | – | – | – | – | – | – | – |
| ILI | + | – | + | – | + | – | + | – | – | + | – | + | – | + | – | + |
| ESI | + | + | – | – | + | + | – | – | – | – | + | + | – | – | + | + |
| LIE | + | – | – | + | + | – | – | + | – | + | + | – | – | + | + | – |
| EII | + | + | + | + | – | – | – | – | – | – | – | – | + | + | + | + |
| LSE | + | – | + | – | – | + | – | + | – | + | – | + | + | – | + | – |
| IEE | + | + | – | – | – | – | + | + | – | – | + | + | + | + | – | – |
| SLI | + | – | – | + | – | + | + | – | – | + | + | – | + | – | – | + |
As one more “proof” of the uniquely correct ordering of the set of TIMs, S. I. Churyumov offers the table of the “Periodic System of the Types of Information Metabolism (represented in the patterns of the socionic square)” [11, p. 390]. Let us show how one can obtain a “new” PSTIM with a table represented in the patterns of the socionic square, differing from the one compiled by Semyon Ivanovich only in the captions, with a different order of TIMs. For this, one need only use the ready-made table of ARTs with the Churyumov sign arrangement (see Table 1). The “coloring” of the socionic-square pattern for an individual TIM is carried out as follows. If a “plus” stands in Table 1 for some ART, the corresponding cell of the socionic square is shaded. The correspondence is given by the coincidence of the ART numbers in Table 1 and the cell numbers of the socionic square.
Table 2. The “new” PSTIM (represented in the patterns of the socionic square). The ART numbers correspond to Table 1.
[For each of the 16 TIMs, in the “new variant” order, a 4×4 grid with cells numbered 0–15 row-wise; cell k is shaded exactly when TIM’s entry in column k of Table 1 is ”+“. ILE has all 16 cells shaded; every other TIM has exactly 8.]
As we see, Table 2 presents the very same information as Table 1, but in a different graphical form. Therefore it cannot serve as an additional argument in favor of a particular order of TIMs. But the main point is that such tables can also be compiled for certain other ways of ordering the set of TIMs. In particular, for all those considered in Fig. 8, with the exception of the Medvedev variant (which is also found in I. Kalinauskas).
Thus it can be stated that the requirement of coordinating the lists of TIMs and ARTs so as to obtain the desired symmetry of the tables proposed by S. I. Churyumov and considered above turned out to be less stringent than the condition of quadral periodicity of the IRs per Augustinavichiute based on the “Churyumov Square.” Of the six variants of ordering the socion considered in Fig. 8, only the last three satisfied that condition. To be sure, one can propose at least one more variant, for which it is likewise easy to order the list of ARTs appropriately so that the already-discussed Churyumov tables with the required symmetry result, and the condition of quadral periodicity of the IRs is satisfied.
If in each quadra of the Augustinavichiute–Liashkiavichius order one interchanges the last and next-to-last TIMs, everything works out. Such a replacement corresponds to interchanging the third and fourth “columns” when the sequence of TIMs in the socion is represented as a 4×4 table. Note that the “new variant” proposed in this work differs from Reinin’s variant by the same interchange of the two last columns.
Which variant of ordering the set of TIMs, then, should be preferred? Can the Augustinavichiute–Liashkiavichius variant be considered better founded because the TIMs located in one “column” of the 4×4 table are ascribed the same role in the quadra after Bukalov? How much better are these justifications than those connected with Savchenko’s symbolic socionics? Must the programmers of a quadra necessarily be extraverts?
Conclusion, or the didactic aspect of the problem
As the investigation carried out has shown, at present there is no complete certainty on the question of which order of TIMs should be accepted by all as irrefutably proved. It turned out that the formal requirements which S. I. Churyumov advanced for the symmetry of the tables he proposed can be satisfied by far more than one ordering variant. The additional condition connected with the quadral periodicity of the IRs per Augustinavichiute reduced the number of admissible variants but did not bring it down to one. The semantic arguments usually adduced are highly debatable. Didactic considerations can help in settling on one variant.
The point is that one usually becomes acquainted with the Jung basis already at the initial stage of studying socionics — before learning about the Augustinavichiute–Reinin traits and about intertype relations. At the beginning of the article it was shown how, relying on the Jung basis, one can unambiguously obtain a sequence of TIMs which withstands certain formal checks without difficulty. As for semantics, it is so far not evident in what way the sequence found is worse than the other variants considered. This makes it possible to propose the “new variant” of ordering the set of TIMs as the most acceptable on didactic grounds.
References
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The article was received by the editors on 26.01.2014.