The Presence Cube

Recently I discovered a new model that is more meaningful than previous models we've discussed.

Any cube model requires three basic traits. The classical Model A cube uses mental/vital, valued/subdued, and evaluatory/situational. The issue is, other than valued/subdued, these dichotomies are not visible in practice. The other variations on the cube all depend on unobservable dichotomies like this.

The most visible traits ⁠in Model A are strength, values, and boldness ⁠— the presence traits. If we use the presence traits as the basis we get the presence cube:

The presence cube for IEI (image credit: Andrew Joynton)

It turns out that this cube gives some very interesting results. We can directly see dimensionality as a projection of the cube onto a certain axis. And there is a directly complementary projection which I call Priority, which defines the most preferred functions in practice: functions 1 and 6, then 2 and 5, then 3 and 8, then 4 and 7. The leading and mobilizing function (the 4P functions) tend to be very visible in someone's preferences, while the suggestive function and creative function are less visible as values due to being cautious (somewhat related to triads). The demonstrative function and role function are similarly used somewhat more due to being bold, although maybe not clearly less than the suggestive function. The 4P and 1P ends do seem to be clear in practice though, much like 4D and 1D functions — so we can think of them as trichotomies, with two extremes and one ambiguous middle region. The middle functions can in fact be lined up by rotating the cube appropriately. So we have two trichotomies and three dichotomies.

The presence cube viewed according to the Priority trichotomy for "Strategic Democrat" types: LIIs and SEIs prioritize Si and Ti and LIEs and SEEs prioritize Se and Te.

The trichotomy for values is linked to the inert/contact (aka stubborn/flexible) dichotomy: the functions at the extremes are stubborn, as their priority does not change easily, and the functions in the middle are flexible: if you rotate the cube slightly the 2nd and 5th functions may fall below the 8th and 3rd ones in priority. Likewise for the evaluatory/situational dichotomy which has the most extreme strengths and weaknesses (4D + 1D functions) on one end, and the medium ones on the other.

The vertical axis in the diagram is sort of a combination of dimensionality and priority, the sum of all three traits which we may call Level of presence, so we get 1L, 2L, 3L, 4L, with the leading function being at the top as the sole 4L function. This roughly describes how much each function is present in someone's cognition and behavior. The 3L functions are the producing functions which are all directly connected with the leading function in some way. The connection the 1st function has with the 4th function is "severed" or veiled.

The LII cube, labeled

The main issue with the presence model is that there is a separate cube for Democrats and Aristocrats (in the Reinin dichotomy sense):

You can reflect the cube in any way to get all the other types with the same Democracy/Aristocracy trait, i.e. either the same quadra or opposite quadra. Rotations are actually unnecessary here; we have 2x2x2 = 8 transformations coming from each reflection / inversion of a trait.

If you project directly onto one of the faces, then you pair elements either as the standard blockings for the given quadras (ignoring boldness), or with one of their "skew blockings" along the benefit ring, ignoring either strength or value. These represent the most common element pairs that we see in practice, since typically rational elements work with irrational ones and vice versa.

The presence cube ties together some fundamental observations from socionics practice and is another significant step towards a meaningful, mathematical model of socionics.

Symmetry Breaking

It's common knowledge that Socionics is a "Ti system." That is to say, Model A and the socion itself are very beautiful, symmetric systems that are, apparently, all-encompassing. This is all well and good, but the theory is also severely imbalanced in this way. It needs to be Te too, not just Ti.

What is a symmetry? It's some kind of change or process that leaves a system looking the same as when you started. Essentially, it's "a change that's not a change". If that sounds like a paradox, it's because it is.

The classic example of symmetry is rotations of a shape: if you rotate a square by 90° it will look the same as when you started — as long as the different parts of the square have no other distinguishing features (such as the numbers in the picture below). It won't be deformed or broken, and will occupy the exact same location in space.

image from http://mathonline.wikidot.com/the-group-of-symmetries-of-the-square

But the right side of the square cannot literally be the exact same as the left side, otherwise it wouldn't have four sides, it would have at most three. If the parts of the square weren't separate and distinct we couldn't even recognize a process as different from doing nothing — except maybe by looking at intermediate states of the rotation, to see that yes, the square is moving from one place to another. In other words, the parts have distinct identities. But in reality identities are only distinguished by observable properties — by Leibniz's identity of indiscernibles, two different things must differ on some property.

The same is true of Model A: EIIs and SLEs are "the same" by virtue of being socionic types, which have strengths, weaknesses, values, etc. described in terms of the same functions and IM elements, but they clearly don't have the same thinking and behavior. If all the types were the same then socionics wouldn't be very interesting. In fact they wouldn't even be types, as everyone would be the same.

Of course socionics acknowledges these differences already — in type descriptions the differences are described, albeit often not very well, or using overly-specific examples drawn from the author's own limited and potentially flawed observations of the type. The real issue is that the differences are not explicit in the theory. There is a mathematical structure describing precisely how the relationships and functions fit together, but there is no mathematical description of, e.g. what makes Te different from Ti. This means that anyone and everyone can come up with their own definitions and say that they're right. Certain ones may fit together better and describe reality better, but good luck trying to convince anyone else to change their minds. So we have a community which is becoming ever-more fractured in its theoretical foundations, with any number of baseless hypotheses being accepted as fact, and passed off as legitimate theory to unwitting beginners.

But in fact there are beginnings of such a mathematical description, partially described right here on this blog. The elements are described by explicit geometric properties like extension (extroversion) and limitation (introversion). A distinct hierarchy emerges: the irrational elements are more fundamental and "wider" ontologically than the rational elements. Irrationality deals with direct apprehension, both physical (the senses) and mental (the imagination and memory). In other words irrationality is prelinguistic while rationality is linguistic. But rationality can be seen as the culmination of the system (and the intellect it describes), and perhaps gives it a greater degree of closure. All of the IM elements are good without a doubt in their own way, but they do play different roles and some are preferred over others in particular contexts.

As mentioned in another article, the contrary elements (Ne and Ni, Se and Si, etc.) are in fact the same information but opposite "vectors" or preferences within it. The dual elements are different, seemingly alien perspectives on the same reality, and our duals open us up to this perspective. The superego elements are arguably the "most opposite" from a higher perspective, but they share certain deceptive similarities and are "far apart" enough that contrary elements will conflict more readily. Conflicting elements can be reconciled in the long-term view but they certainly conflict in the here-and-now, as opposite states or choices (which produce said states).

That's roughly how it goes for IM elements. What about types? One benefit of 16-function models is that they identify types with IM elements, and therefore also functions with relationships. "Introverted socionics" further identifies types with relationships. Taken together, they will theoretically unite the basic elements of socionics into one fundamental reality, which manifests itself in different forms. It just so happens that IM elements are at the forefront of what we can describe in detail, because they are what we actually observe (i.e., information). So if you want to understand socionics, understand the IM elements.

Quadrality and the Theory of Triads

Socionics is indisputably based on quadrality. Because it's built on dichotomies, everything is groups of two, then four, eight, sixteen (4 times 4), and so on. Model A is conventionally depicted as two rings, and for the types we have supervision and benefit rings, quadras, clubs, and so on. But what has not been mentioned up until this point is that, in practice, these groups of four (whether they are types, functions, elements, etc.) often manifest as groups of three - the fourth one remains hidden.

Example 1: Among the valued functions, the suggestive function is often out of sight, due to being weak and cautious. While it is an unconscious goal, people rarely prioritize it in practice - it's as if they are unaware that they need it. The remaining values (functions 1, 2, and 6) are manifest values.

This leads directly to the sub-example of quadra triads: you rarely observe that someone is, e.g. "Gamma" - there is always a bias in the information towards some subset of the quadra, such as the "Fi Gamma triad" (excluding LIE who has Fi suggestive), the "Ti Alpha triad" (excluding ESE who has Ti suggestive), etc.

Example 2: Among the strong functions, the ignoring function's goal is sometimes neglected to the point where it looks weak, due to being both subdued and cautious. We can use it when needed occasionally, as it's less stressful than the 1D functions, but not much beyond that. So, much like the suggestive, the lack of these two traits "overpowers" the presence of the third. This leads to club triads, e.g. the "Fe SF triad", the "Ni NT triad", etc. The remaining strengths (functions 1, 2, and 8) are manifest strengths.

Example 3: Among the weak functions, the mobilizing function is both valued and bold, so while clumsy and overconfident, it can be the "slow and steady one that wins the race", often developing habits over time that allow us to achieve its goal adequately for ourselves. The remaining weaknesses (functions 3, 4, and 5) are manifest weaknesses.

Example 4: The creative function, although cautious, is used with far less fatigue than the other cautious functions, to the point where it works together with the leading function amicably.

Example 5: All of the producing functions can be "blocked" with the leading function to define the type, however the vulnerable function is much more rarely used in conjunction with it. Similarly it is the one left out of the mental ring, being almost completely neglected compared to the others.

There are plenty more examples on the semantic side, to give a few:

• Ti is the structure of language. Te is the objective information conveyed via language, and Fe is the implicit aspects of communication through language. Fi's relation to language is less obvious.
• Se is "completely apparent" while Ni is "completely hidden", and Si is the balance between the two.
• The Enneagram instincts roughly correspond to Si (self-preservation), Fe (social), and FiSe (sexual). Here we have two which are grouped together instead of one being hidden.
• Se is the most masculine of the irrational elements, Si the most feminine, while Ni and Ne seem to lack gender for the most part.
• The themes of aesthetics and beauty involve Si (pleasantness, good taste), Se (outward appearance which conveys status, impact and impressiveness, and sexual attraction), and Fe (adornment and expression through choice of fashion). Fi again seems to be absent.
• Alpha is the quadra of unity (harmonious communal interaction, understanding the universe as a whole), Beta the quadra of duality (good fighting against evil, us versus them), and Gamma the quadra of multiplicity of independent things, facts, or people. Delta seems to have no particular attitude with respect to number.
• If you take all four irrational elements (or all four rational elements) you can make a square with the opposite points being either duals, extinguishers, or superegos. But you can't make them identicals since that would imply repetition.

There are even more examples beyond socionics:

• If you imagine two lights which are either on or off, we can have 1) both on, 2) only one on, or 3) both off. So four possibilities lead to three by the act of counting, i.e. by identifying the two lights.
• The one who speaks can be either truthful or a liar. The one who does not speak is merely silent.
• A car can veer off to the right, to the left, or stay on course. Its motion prevents the backwards direction from manifesting.
• An action is either in the past, present, or future. When past, you find yourself after the end. When future, you're before the beginning. In the present you're after the end and before the beginning. But you can't be before the beginning and after the end.

FOUR FROM THREE

A mandala from Jung's Red Book

Jung was particularly prescient on this topic. He would create mandalas, a kind of four-fold diagram made of a square or cross combined with a circle. He interpreted this as an archetype of wholeness, unification of opposites, and eternal evolution and rejuvenation of the Self. The triad is by comparison incomplete, deficient:

"We find a wide spectrum of four-fold symbols and systems in religion, myth, history and culture. There are four winds (Boreas, Eurus, Notus, Zephyrus), four seasons (winter, spring, summer, fall), four directions (north, east, south, west), four Evangelists (Matthew, Mark, Luke, John), four letters in the sacred name of God (YHVH), four ancient ages (gold, silver, bronze, iron), and four medieval humours: sanguine (blood), choleric (yellow bile), phlegmatic (phlegm), melancholic (black bile)to name a few.

Adding a fourth to an already established three has a transformational effect. In geometry, a fourth point transforms the two-dimensional triad or triangle into a figure with depth, the cube and the tetrahedron (a form lapis). As the mathematician Michael Schneider observes, “There are always four ways (another quaternity) to look at any three-dimensional structure: as points, lines, areas, and volumes, or as corners, edges, faces, and from the center outward (63). Ellenberger notes that “The quaternity can appear as a geometric figure of square or sometimes rectangular shape, or it will have some relation with the number four: four persons, four trees, and so on. Often it is a matter of completing a triadic figure with a fourth term, thus making it into a quaternity” (712). Jung searches for the quaternity when a trinity is encountered, “Jung over and over again in his writings returns to the alchemical question: “Three are here but where is the fourth?” (Edinger 189). The completion of the quaternity is seen frequently in alchemical works, even whimsically, “All things do live in the three/ But in the four they merry be” (quoted in CW 12 125)." [Source]

 Augusta may have been inspired by this to complete Freud's triad of ego, id, super-ego with "super-id" (although the analogy with the actual functions is a bit weak).

Dualization itself is completion of the four quadra values from two overlapping threes, where your leading function completes your dual and vice versa.

The theory of signed elements completes the three function dichotomies with a fourth, to produce 16 functions.

But socionics as a whole is based on Jung's four functions and is in this sense already complete. So the question becomes, how do we derive the three from the four, the appearance from the reality? Each triad is such a derivation.

"The goal of psychic development is the self. There is no linear evolution; there is only a circumambulation of the self" (Jung, MDR 196)

Model G and How To Fix It

Jack Aaron and Ben Vaserlan recently had a heated debate over the relative merits of Model G and Model A: why Model G was created and if the reasons really hold up.

Aside from a few minor quibbles (such as the supposed difficulty of telling apart the vulnerable and role functions), I completely agree with Jack's criticisms of Model G. In short, it adds essentially nothing to Model A, is steeped in vague jargon (like "long range" and "short range", the social vs. personal spheres, etc.), and is at odds with how the types actually work (in particular how it conceives of the suggestive function as being somehow "high energy" or more prominent than the mobilizing function — or whatever they're called now).

Model G does, however, have a few selected insights. One is the greater emphasis on the benefit rings, or rather, the bold/cautious dichotomy.

Another is the idea of "energy." For some reason Ben flounders in this video when asked to define energy, while he had previously connected it to Jung's concept of libido (not Freud's), which Jung defined as a kind of "life force". This is a sound idea in itself: Model A addresses information processing (information metabolism) but it does not address the obvious limitations of resources that apply to each function's processing, in particular the strength and boldness traits.

Unfortunately, beyond this very basic outline, the details of Model G seem disconnected with the reality of the types — including which functions are supposedly maximum energy, etc.

That's a very brief take on the semantics — the details are really not that interesting and are addressed in the video. Another interesting idea (which precedes Model G) is the signed elements, but I'm not going to get into that here either. The real point of this post is the structural deficit which I pointed out and Jack later mentioned in the debate. It's very obvious if you look at Andrew's diagrams (and translate the names and numbers accordingly):

As you can see here, some of the standard socionic dichotomies are presented asymmetrically in Model G. Gulenko apparently does not assign any meaning to the left and right sides of the model, he still uses the standard dichotomies such as strong/weak, etc., albeit with different names, as displayed on the right here. Strong/weak becomes "master/slave" and valued/subdued becomes "values/tools". (correction: It is said that Gulenko does consider the left-hand functions to be "better" in the "sense [...] of energy allocation to the function and the degree of freedom of behavior afforded by this." Again, more jargon which does not seem to apply to the suggestive function, or if not actually wrong, at least is not as clear as the existing Model A dichotomies.)

How can we fix this? The obvious thing to do would be to simply switch the suggestive and ignoring functions (or "manipulative" and "control", numbers 6 and 8). Then the left side is strong and the right side is weak. And the valued functions are "outside" and subdued "inside", which is at least as good as it is in Model A. And we still have the benefit rings proceeding horizontally: NeTeSeFe... and TiNiFiSi....

In my opinion this clearly shows that the Model G blocks are defined wrong. The issue is that Gulenko wanted to have a benefit loop of types, but he represented them using the standard Model A ego blocks (as the columns of Model G). So for ILE we have NeTi, then TeSi, then SeFi and FeNi for the ILE and its Process-Extrovert ring. Instead we should express the types entirely in terms of the benefit ring (in analogy with how it is in Model A and the supervision ring) with each represented using a consecutive pair of elements in the ring, ILE being NeTe, LSE being TeSe, etc. Then the types can be thought of as "edges" between the IM elements, and they interact at their shared points. This makes much more sense if Model G is meant to show energy flow, does it not?

Ben made the interesting point (possibly the only one he made in the entire video) that Model G includes not only benefit rings, but also supervision rings if you extend it vertically:

(Written in to the left of the #4 heading.)

Note that this property still holds if we switch the suggestive and ignoring functions. There are literally only two ways to make a grid like this, and Model G does not use the right choice.

Aside from the semantic issues with Model G, this is a very obvious structural flaw. Fixing it might be the first step to salvaging the model.

Meaning and Mathematics

Socionics, like other scientific theories (in particular physics), relies on giving meaning to mathematical structures: the elements of a group are interpreted as relationships, and they act on elements of another set which are interpreted as types, etc. While proving things about mathematical structures is helpful for "mapping the structural landscape" and getting a sense of what is or is not possible, it must be complemented and guided by an understanding of what the structures actually mean. This is true even of supposedly "pure" mathematics. Often mathematicians have a vague sense of this, but only enough to "get by" — the deeper meaning is left untouched.

To see what I mean, consider an interval:

We can interpret this as being a scale, where one end is, say, hot and the other end is cold.

Then, if we bend and join the ends of the scale to make a circle:

Hot and cold then occupy the same place. But isn't that a contradiction? How can two opposites be the same?

In fact this "unification of opposites" lies at the very heart of socionics. For what is a dichotomy (like sensing-intuition or logical-ethical) itself if not a union of opposites?

We can then notice that, on a semantic level, what the two ends of a scale have in common is that they are both extremes, while the middle of the scale is balance or an equal combination of the two extremes:

So we have obtained a new scale -- which is none other than the distinction between Se (extreme) and Si (balance)! Or at least one major aspect of it, anyway.

Since any pair of binary opposites can be placed on a scale like this — including Si and Se themselves! — we see that socionics touches on some of the deepest and most universal structure of reality — that point where geometry, meaning, and structure all meet, and produce a self-describing model of reality.

Readers may recognize these concepts from any one of various ancient traditions: Sufism, Hermeticism, sacred geometry, etc. All we are doing here is fleshing them out using the language of mathematics.

The full consequences of this remain to be seen.