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Introduction
In my time on the CT server, I encountered an array of conversations on the expression of quadra values; most peculiar to me was a particular method of quadra analysis that wasn't quite based on direct comparison between the mechanical components of each quadra (the usual analytic approach to deriving similarities and relations), but rather, there seemed to be an inductive hypothesis based on observations of vultologically typed people who had entered and exited the community. I will eludicate the nature of these perceived conceptual similarities in this post, however, in order to understand these similarities, I think that it is necessary for there to be at least a formal or semi-formal derivation; if each step is explicated, and the causal links between the steps are shown, the relations between the quadras which have largely so-far been "vibe" based and inductive can be formalized and explained by the composition of each quadra. Note that I am not necessarily saying that "vibes" are bad, I am saying that if these "vibes" are explained formally, then a newcomer to CT, or even just someone interested in the theory would know not only how they come to be (because they are explainable phenomena in my view), but also be able to employ them as useful heuristics for type analysis. However, in order to understand the origins of the quadras, it is necessary to start from a theory that precedes CT, the theory from which the idea of a quadra originated - Socionics.
Socionics is a theory of psychological type which was created by the Lithuanian professor of sociology Aushra Augusta, who sought to model human relations through a consistent abstract structure; her approach to this combined two theories which originally had rather different purposes, Carl Jung's theory of psychological types (which attempted to paint a portrait of each of the patterns that he had observed across his patients and labelled "psychological types", and Antoni Kepinski's theory of information metabolism, a theory formulated to describe the divergences between the way each species treats environmental input internally. Straight away it's apparent that Jung's theory concerns externalized phenomena; he begins from observations, points a detailed observational portrait of each type, but in the absence of observable phenomenological aspects of each of his psychological types (beyond what he inquired of his patients), it is apparent that Jung's speculations were left in a state of tentativeness, certainly not definiteness and certitude (the status of many of his abstractions, partially due to his noncommittal attitude to extrapolation, and partially due to a very vague and esoteric writing style, is difficult for an observer to to determine). This approach is quite opposed to Kepinski's; indeed, the observation for Kepinski only serves as a starting point, from it follows a complete structure whose components are perhaps not viable by empirical observation or even the scientific method more generally (a common criticism of his work is actually that it is unverifiable). Aushra decided to take Jung's psychological types and arrange them from the perspective of Kepinski's theory, that is to say, each psychological type was taken and from it extrapolated a theoretical description of the internal process leading to Jung's portraits (like external object dynamics being used as notation for his extroverted thinking type, for example) and the metabolic attitude towards each process. The arrangement of these attitudes by prominence and priority is known today as Model A.
Why quadras?
The combination of the more phenomenological approach laid out by Kepinski and the more observational approach laid out by Jung has some interesting consequences. One needs a basis point from which to anticipate these consequences, in this case, the basis point for extrapolation would be the intention behind the creation of Socionics; as indicative by the name of the theory, it was created initially to model interactions between people in a structural manner. The model for the individual was based on Jung's portraits applied as information elements; or pieces explaining certain kinds of information and focuses towards or away from these kinds of information (where the hierarchical arrangement of all the information elements in terms of focus yields a type). These arrangements in isolation are referred to as types; and presumably people have a best-fit type which explains some of their cognitive and behavioral tendencies (which also allows us to make a digression about an important aspect of Socionics, which is that it is not centrally a theory of only metabolism, but also one of interaction). It only becomes Socionics, however, when one proceeds to explain through the frameworks how various individuals interact with one another; given that the type is the Socionic method of expressing an individual's tendencies, and types are formed from hierarchical arrangements of information elements (with the interactions between these elements also explained as a part of each type, and generalized to apply across types). It follows, thus, that the structural descriptions of the relationships between types (and thus also the individuals of each type) are based on generalizations about the nature of the interactions between the various information elements. The theory of intertype relations is based on explaining information element interactions; the basic principles are centered around elements "balancing" other elements out.
For example, a Te base type in Socionics also by definition values the other end of their rational axis, which is in this case, Fi (valuation in Socionics is based around two axes, the valued rational axis (conceptually equivalent to CT's J functions), and the valued irrational axis (conceptually equivalent to CT's P functions)). This means that there is the assumption that Te base types necessarily be receptive to Fi, and that the relation of duality (or the relation that has the greatest mutual ease of information transfer) for the Te base type would be a relationship with the Fi base type. Of course it becomes important to account for the irrational axis and the consequent Jungian dichotomies of the type. For example, a Te base type, with the irrational axis Se/Ni must also have a creative introverted irrational function, and because their irrational axis is Se/Ni, this function is Ni, meaning that their Jungian intuition/sensing dichotomy yields an intuitive preference, and meaning that their overall strength at all aspects of intuition are greater than their overall strength at sensing. This knowledge allows us to calculate the compatibility that this Te base with the Se/Ni irrational axis will have with both Fi bases - and because the Fi base with Se/Ni compensates for the weak sensing of the Te base (unlike the Fi base with Ne/Si, who is also an intuitive type, and thus doesn't make that compensation), the relationship with the Se/Ni Fi base yields greater compatibility (as Socionic notions of compatibility are based on mutual compensation).
This means that for each set of valued functions (a set of valued functions is composed of four functions), there will be 2 dual pairs (full primary axis compensation), and 2 activator pairs (semi-compensation through the the creative function of the dual type's mirror, which has the dual's base as the creative), and thus four types that share this set of valued functions. For these four types to be properly composed (with one rational axis and one irrational axis), the quadra's set of valued functions must also be comprised of one rational axis and one irrational axis. This yields four possible sets of valued functions which quadras emerge from; Ne/Si and Ti/Fe (Alpha), Se/Ni and Ti/Fe (Beta), Se/Ni and Te/Fi (Gamma) and Ne/Si and Te/Fi (Delta). Each of the quadras will have one pair of rational types (with a primary rational function, which can be either an extroverted rational function or an introverted rational function), and one pair of irrational types (with an introverted or extroverted base functions) that form two dual pairs. We can say that quadras which have opposite rational and irrational axes are opposite quadras; this means that Alpha and Gamma form one opposite pair, whereas Beta and Delta form another opposite pair. Thus, our derivation of the four quadras from the basic Socionic concepts of information interactions is concluded here (if you would like to see a more formal mathematical derivation of the quadras in Socionics, along with the rest of the theory, check out this link )
CT also employs these same quadras, with the same names and even the same functions shared between them. However, CT's quadras cannot be derived from the relationships that exist between types (as pairs of rational/irrational axes), as CT lacks two assumptions that Socionics makes in this realm; the first assumption CT does not make is that rational/irrational pairs are mutually compensatory (Auburn's own post on intertype relations seems to suggest subtly that perhaps the polar function is not always something that's regarded highly), and the second assumption that CT does not make is the assumption that relationships between functions can be expressed deterministically or mathematically at all (because Auburn, in an effort to keep this model observational and empirical, has attempted to reduce the presence of deterministic monoliths). Therefore, to derive the quadras in CT, a different route has to be taken. The axiomatic building block that Auburn has chosen to use for CT (as opposed to the information element and the interactions between the information element) is the energetic. There are four energetics in CT, Je, Ji, Pe, and Pi. The Je and Ji function in an individual forms their J axis (also referred to as a J oscillation) and the Pe and Pi function in an individual forms their P axis (also referred to as a P oscillation). The presence of both of these oscillations in the individual is a given, and the polar function of an individual is of the opposite orientation to their dominant function, i.e, dominant Xe always means polar Xi, dominant Xi always means polar Xe. And since they exist as oscillation pairs, the polar function is the other half of the oscillation of the dominant function, meaning dominant Je always means polar Ji, and dominant Pe always means polar Pi. Note that unlike Socionics; it is not a relation of interaction, but implication.
CT's four macrofunctions are intuition (N), sensing (S), thinking (T) and feeling (F). The intuition and sensing function present in a person forms their P axis (or P oscillation), and the thinking and feeling function present in a person forms their J axis (or J oscillation). An energetic is just an externalized disposition; on its own it is inert, combining an energetic with a macrofunction results in an entity that is descriptive of a kind of information and the internalization or the externalization of this information. This entity can be referred to as a function. Now, among the four energetics, two of them deal with J (judgement), and two of them deal with P (perception), and we see that the macrofunctions are the same way. Just like we can't add numbers expressed in different units, we can't combine energetics and macrofunctions that deal with different kinds of information; this means that a J energetic can only be applied to a J macrofunction, and a P energetic can only be applied to a P macrofunction. This means that there are eight possible combinations of energetics and macrofunctio, which are as follows:
Given that intuition and sensing form a pair, and introverted and extroverted functions form a pair, we can derive two oscillations of functions (as opposed to energetic-socillations, which are implied in function oscillations, functions being a derivative of energetics and macrofunctions),the Ne/Si axis (Pe + N and Pi + S), and the Se/Ni (Pi + N and Pe + S). The term axis is being used here as opposed to oscillation to reduce confusion (as axes are oscillations of functions, not macrofunctions or energetics). Given that thinking and feeling form a pair, and that introverted and extroverted functions form a pair, we can derive two further oscillations of functions, the Te/Fi axis (Je + T and Ji + F), and the Fe/Ti axis (Ji + T and Je + F). Keeping in mind that each type can only have one of each axis; because each type has four functions, and because all types must have one of each kind of function, we come to the same four groupings of the 16 possible types in CT as we do in Socionics; the types that have the Ne/Si and Ti/Fe axis are known as the Alphas, the types that have the Se/Ni and Ti/Fe axis are known as the Betas, the types that have the Se/Ni and Te/Fi axis are known as the Gammas, and the types that have the Ne/Si and Te/Fi axis are known as the Deltas. Thus, it has been demonstrated that quadras an axiomatically necessary feature of CT as they are of Socionics.
The energetics and the macrofunctions
One last aspect that we'll have to define before we can begin to explore the emergent properties of each quadra; the energetics and the macrofunctions themselves. These are best understood. in my opinion, by defining the fundamental properties of each four of the functions; these are similar to the Jungian definitions of the functions. I will be taking a conceptual divergence from Auburn regarding the nomenclature, however, by limiting the kinds of information that each macrofunction deals with differently. I am of the view that J macrofunctions construct models abstracted from the situations themselves, and the situations which serve as inputs for the models are regarded with less precedence than the idealized models themselves. The P macrofunctions, on the other hand, while they can be divorced from concrete observations, do not actively seek to meld perceptions to a constructed ideal or system, and so rather than operating from models, the P functions operate as webs, where perhaps there is an inter-linked chain of perceptions but little when it comes to a consistent axiomatic basis tying them together. Now that the broadest dichotomotus distinction has been drawn, we can proceed to draw the distinctions between each macrofunction. Thinking is a J function, which means it constructs models and prioritizes these models; feeling also constructs these models. The difference here is not one of precision (most J functions desire a degree of precision in their expression regardless) but the animation of the inputs; F treats its inputs as interacting not only mechnically but intersubjectively (as if each input is a subject), whereas T does not. This means that F inherently requires a situationalism that T does not have; a perception of contextual cues is necessary to see subjects as they are and expand judgements from there; T does not have this situationalism. This is why I consider F situational and T removed. Moving on to the P macrofunctions, which are intuition and sensing. The conceptual difference between these two is that sensing deals with literal information, whereas intuition deals with associative information; this means that sensing is usually concerned with gaining a view of the thing-in-itself essentially, intuition is concerned with viewing a thing by permutations of what it could be or what it may be tied into. The potentialist view of intuition leads to a greater proclivity towards generalization, whereas sensing tends to have a specificity to its view. Note that both can be intellectual; it depends simply on the manner of exposition, this is usually what yields the N/S status. The energetics are roughly much more straightforward than the macrofunctions; Je seeks to explain etiological relations between objects and establish them in an exteranlly explicable form (hence, formal logic), Ji seeks to explain atemporal and aspatial essential properties of of an object and express these properties in a self-contained encompassing form (hence, semantic precision and essentialism), Pi seeks to understand pertinent historical shifts in understanding/perception and attune itself to temporal fluctuations, whereas Pe seeks to engage wholly with its object of focus with no burdens external to this pursuit.
Constructing quadras with macrofunctions
We take a step back now to think again about the etiology of quadra; only in this case we attempt to understand quadras and their emergent properties through a combination of the macrofunctions. Recall that every type has a J axis and a P axis, and that all types in a quadra share the same functions, therefore every type in a quadra shares their J axes and P axes. This means that all types in a given quadra will be expressible in terms of the other types in that quadra, and no other forms (at least if we are referring to formal expression, we are not accounting 'vibes' here). The existence of polar types within the same quadra also means that these expressions can be understood as pairings, that is to say that within each quadra there will be two pairs of types with their functions in opposite orders. This means that if a quadra contains a type with lead N + aux T, then the quadra must also contain a type with lead S + aux F (and to configure the functions by their two other orders, the quadra must also contain a lead T + aux N and lead F + aux S type). This means that quadras are limited to certain combinations and must restrict others in order to retain their properties. We can now begin to elaborate tentative models of two main kinds of quadras; N+F-S+T quadras, and N+T-S+F quadras (these are technically not yet quadras, because until we apply the energetics to them, there are only two of them, but the application of the energetics to these quadras makes the presentation of quadras with the same combinations as far more different than they actually are).
Quadras with N+T and S+F can be characterized as possessing two distinct kinds of combinations; going by the dichotomies estbalished above, we know that any N function is generalizing rather than specific (leading to larger abstractions), and we know that any T function is removed rather than situational in its consideration of the status of objects (leading to less involved axioms). The two functions share this property; at the same time, they differ in another property, in that while N itself is the antithesis of literal expressions, T does express its removed truths in a literal format (becuase of a lack of considerations of situational "movements" of each party that F possesess), meaning that the two aspects conflict in the sense that while N seeks to associate, T seeks to limit. We can see that the S+F combination has a similar aspect to it, while S seeks to express objects non-associatively as literals with account for their directly observable processes, and while F is also situational in its consideration, F's situationality stems from evaluations of inner "essences" weighed around moving/non-moving aspects of its objects, meaning that S+F also has an inherent contradiction; while both components are involved; F's biotic considerations can contradict S's views of literals. We can generalize these analyses to a few properties of the N+T-S+F quadras, both sides of the quadra are characterized by either an extreme abstraction or an extreme involvement; but the asymmetry this causes leads both sides to also possess a sense of incompleteness or ambivalence; and perhaps a greater subjectivity to judgements (or percieved subjectivity, due to a preference for one extreme over another).
Applying the energetics to the N+T-S+F quadras yields the Alpha quadra and the Gamma quadra respectively; because they extrovert and introvert completely opposite combinations (Alpha extroverting N+F and thus holding a greater attentiveness and receptivity owards N+F, Gammas extroverted S+T and thus prestending themselves as practical and hard-headed), the combinations on one side of the quadra despite their orientations will be the same. Thus we can say that Alphas and Gammas which have N+T as one of their first two functions (or a combination of either Te+Ni or Ti+Ne) are unable to accurately situationalize their judgements (leading to a one-sidedness in their views, hence the perception of both Alpha revisors and Gamma conductors as subjective), whereas the Alphas and Gammas that have S+F as one of their first two functions are unable without the presence of the other two functions to generalize and may seek to express information in a highly specific format (and generalization is important, meaning that Alpha conductors and Gamma revisors too, can be seen as too subjective). Due to the distinct clash between situationalism and universalism, we can establish the main property of the Alpha-Gamma dichotomy lying in asymmetric oscillation. For Alphas and Gammas, this also often manifests in epistemic skepticism, or what @jelle has called the "Galpha" propensity; the imbalance leads to a lack of knowing. What this also means, however, is that these quadras dispositionally may be less prone to normative judgements; and perhaps even more cautiousness in thought.
Quadras with N+F and S+T on the other hand, dichotomously speaking, have a different structure. S+T are both literal macrofunctions, meaning that they express information in the same form fundamentally, on the other hand, S is situational and T is removed, meaning that the elemental combination of S+T is complementary. On the other hand, N+F are both non-literal macrofunctions, meaning that they deal with information that cannot perhaps always be literally expressed (and may require associative or allusory interpretation), but on the other hand, F is situational while N is generalizing, leading to another complementary pair. This complementary ostructure to each type's function-structure usually yields a good balance of objectivity and subjectivity; a person that belongs to this quadra is somewhat natively likely to be able to see things from both sides of the coin and come to a neutralized judgement; more importantly, this also means that individuals who belong to these quadras are broadly less likely to have a neurosis over the epistemological status of their views; because the skew isn't one-sided, they are more likely to have a greater confidence in their views, and these include moral imperatives; to the point where informally, those on the CT server who are seen as morally consistent and epistemically certain are referred to as Beltas. As you know, the application of the energetics to this macroquadra results in the Beta and Delta quadras; which manifest differently in terms of behavior and occuptation (oppositely energetically oriented functions), but somewhat similar epistemically. These quadras have symmetric oscillations.
To summarize, I will outline the properties of each quadra pair below:
The N+T-S+F quadras (Alpha & Gamma):
The S+T-N+F quadras:
There's so much juicy stuff here that I am so frustrated at myself for not being able to address! The idea of macrofunctions properly picks up on the way the CT model is arranged, and the formulation is very near to my own thoughts as well. Your explanations help me clarify some of my own ideas and to understand how to better structure the model.
And if I wasn't so busy fleshing out the pages for model 2 atm, I'd give this a proper reply. But I will have time soon. I am shooting to have the preliminary skeleton to model 2 ready by this Monday, and will make it live (as a work in progress), at which point I will come back to this and some of your other recent posts.
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