The Model A cube

Note that Augusta actually was aware of this cube and mentioned it in a 1985 article on the Reinin dichotomies. However, the idea that the relationships are transformations of the cube was not mentioned.

Model A is generally presented as a linear, 1-dimensional model, or as a 2-dimensional grid. You have functions 1, 2, 3, 4, 5, 6, 7, 8, also known as leading, creative, role, etc., which can be arranged in two different "loops".

But in reality, Model A is neither a line nor a grid. It's a cube. It is not 1-dimensional or 2-dimensional, but 3-dimensional.

That is to say, you can arrange the functions of Model A like so:

And when you do, the intertype relationships become symmetries of the cube. The top and bottom faces of the cube are the mental and vital loops.

Let's say that this placement of the cube represents LII, so that the closest bottom edge represents the ego block, with the leading function on the left. Then

-the duality relation is the vertical reflection (switching TiNe with FeSi)
-supervision is a 90 degree rotation about the vertical axis
-mirror is a reflection across the yz-plane
-comparative is a reflection across a diagonal plane
-extinguishment is the antipodal map / complete reflection which sends each point to the point opposite from it

Supervision can be replaced with benefit as the rotation to produce a "Model G cube" as it were, making the benefit rings apparent instead of the supervision rings.

Duality can also be replaced with extinguishment as the vertical reflection.

And comparative can be replaced by any of the "odd" relations - the ones that reverse the Process/Result dichotomy.

These three choices determine the model, so that there are 2*2*8 = 32 versions. The one above is the "dsk" (dual/supervision/comparative) cube. In all cases, the possible transformations are exactly the ones that preserve the cube itself and preserve the vertical axis. Half (eight) of them reverse the cube's orientation and half of them preserve it. In the dsk cube the orientation corresponds to the Negativist/Positivist dichotomy.

The diagonal reflection (which is the comparative relation in Model A) fixes half of the functions. We can expand the cube to a 4D hypercube, and Model A to a 16-function model, so that no relation fixes any functions:

In this case we can actually identify the types with the IM elements. I interpret this to mean that each type has an overarching goal in life, which is the leading function. Typically these are written as "signed" versions of the regular IM elements:

+Ne	ILE
-Si	SEI
+Fe	ESE
-Ti	LII
-Fe	EIE
+Ti	LSI
-Se	SLE
+Ni	IEI
+Se	SEE
-Ni	ILI
+Te	LIE
-Fi	ESI
-Te	LSE
+Fi	EII
-Ne	IEE
+Si	SLI

The elements of Model A (and any other cube model) are coarser versions of these elements, e.g. Ti is just +Ti and -Ti (LSI and LII) grouped together.*

Because types are identified with IM elements, in the 4D model we can simply choose which relations are adjacent to the type:

-(beneficiary and benefactor) or (supervisor and supervisee)
-one of the odd relations
-extinguisher or dual

There is much more to say about the cube, but this will do for now. This is the perfect logical system underlying socionics.

* Notice also that although the look-a-like relation is also a diagonal reflection in the Model A cube, it technically defines different elements than the comparative relation: Reasonable EJ, Reasonable IJ, Merry EP, Merry IP, etc.

Empiricism

Ti valuing types are sometimes criticized for ignoring empirical data if it is not consistent with their views. The argument, so it goes, is that empirical data is real or factual, and views can be changed, therefore the empirical data takes precedence over any prior belief that one may have concerning it.

While this is true, it can be misleading if taken too far, and in fact seriously impeded the progress of science on different occasions in history. One is the discovery by Galileo (ILE) that all objects in free fall will fall at the same rate. Typically if you drop a feather and a bowling ball they will not fall at the same rate. But as we now know, this is due to special conditions that exist on the Earth's surface (air resistance) and in no way contradicts the more basic and fundamental truth. Galileo presented an argument to this effect, but it is said that he did arrive at this fact empirically, by cleverly choosing an experiment in which air resistance wouldn't be a factor. The whole idea of doing controlled experiments in fact does mean "ignoring facts" or rather assuming a certain model of the world, in which the other factors are thought not to matter. (An assumption which may not be valid depending on how the experiment is set up.)

Another example is the Copernican model of the solar system (or rather the universe as it was known at that time). In fact the Copernican model was not much more accurate than the Ptolemaic model, although it did require fewer epicycles. The backlash it suffered is not unlike the reactions faced by proponents of speculative or revolutionary theories today, even if the one was supposedly based on religious dogma and the others on hard-nosed skepticism.

What this suggests is that reasoning from facts (Te) is not enough. One may also reason based on ideas or pure logic (Ti, with intuition). The most extreme example of this in the history of science is the theory of general relativity by Einstein (also ILE). Unlike quantum mechanics, which was cobbled together from various different observations, and whose interpretation and principles are still in dispute, Einstein started out with a clear physical principle: the laws of physics should be invariant under smooth changes of coordinates. Since there are many different ways of describing the same situation with different coordinates, it should not matter which ones we use. To this he added some empirical requirements, like reproducing Newton's laws in the limit — but in fact, he too was misled by this! He became stuck, trying to reconcile the idea with the "empirical" data. It was not until he realized that in fact coordinate invariance was the primary requirement (and the so-called facts required subtle modification) that he finally completed the theory. Empirical evidence for general relativity actually remained somewhat scant for many years. Another point to note here is that it is easy to confuse an interpretation of the facts (like a "proven" past model) for the facts themselves. All observations except the most basic are tied up in some way with interpretation.

So, as one might expect, the approach I (LII) use to develop socionics uses a great deal of a priori reasoning (while of course making use of both). It's like you have two masses, one consisting of knowledge that is known to be true by reasoning, and one consisting of all observations of the world. You can then bring them together by moving either point towards the other, or both, until they meet in the true model. In fact, a priori truths may seem disconnected or cover different domains (like general relativity and quantum mechanics), and themselves require unification. Our basic physical understanding of the universe has been stuck for decades, and what we need to move forward is a thorough re-examination of the concepts underlying the theories, starting with what is absolutely clear and building on top of that until everything has been "digested" into an indisputable form, or else cast aside as remnants of past confusion. This is a huge task, but it can, and will, be done.

Becoming your benefactor

Your benefactor can be seen as a "better version of you" -- someone who does something similar to what you do, but more effortlessly, and can go beyond your limitations. A big part of self-development consists of learning how to use the demonstrative function in conjunction with the suggestive function, or we may say in terms of Model A2, using the progressive demonstrative function (p8). Someone who does not do this can conversely seem myopic or naive.

Some examples come from the theory of integral types.

The computer programming community is essentially an ILI in its approach. Formal methods and principles are considered but generally take a back seat to pragmatism. The most extreme examples are in the Linux-based "hacker" community, which evolved into the open source community, and is notorious for its toxically critical culture and neglect of the subjective experience of using software (user experience aka UX, an Si domain -- more likely with Fe), as opposed to how it gets things done.

However, this approach has led to a crisis: software now, and in particular the most widespread software like operating systems and the internet, have become such a complicated mess that major companies are being hacked on a regular basis. The way out of this situation is to make systems that implement formal verification and strict systems of access control from the ground up. The internet largely grew organically and without a clear view of what the system would or should look like later on. It's debatable whether or not this situation can be resolved, but an LSI approach is what is called for.

Another crisis is in the mathematics community. The world produces a large amount of formalistic mathematics, consisting of jargon like "for every complete valued extension k′ of k, the higher coherent cohomology of X×k_k′ vanishes." (real example taken from arxiv.org) Often mathematicians themselves are unable to assign intuitive meaning to these terms. While this may not be seen as a problem from inside the math community, it poses serious problems for anyone who seeks to apply math to reality, like physicists. We need to go back and find some kind of holistic, unifying meaning for math -- in short, use +Ni, the Ni of the IEI. (Debatably "meaning" here also includes Ne, in the sense of intuition as used by physicists.)

Some ideas of Jung

I must confess, I have never read completely through Jung's Psychological Types, or even the chapter that is about the type definitions. I find the writing to be often convoluted and not very much related to socionics as it stands today. Perhaps the best part is the description of extroversion and introversion:

"The relation between subject and object, considered biologically, is always a relation of adaptation, since every relation between subject and object presupposes mutually modifying effects from either side. These modifications constitute the adaptation. The typical attitudes to the object, therefore, are adaptation processes. Nature knows two fundamentally different ways of adaptation, which determine the further existence of the living organism the one is by increased fertility, accompanied by a relatively small degree of defensive power and individual conservation; the other is by individual equipment of manifold means of self-protection, coupled with a relatively insignificant fertility. This biological contrast seems not merely to be the analogue, but also the general foundation of our two psychological modes of adaptation, At this point a mere general indication must suffice; on the one hand, I need only point to the peculiarity of the extravert, which constantly urges him to spend and propagate himself in every way, and, on the other, to the tendency of the introvert to defend himself against external claims, to conserve himself from any expenditure of energy directly related to the object, thus consolidating for himself the most secure and impregnable position."

That is, maintaining vs. propagating the self. This fits completely with socionics extro/introversion, and in particular Si and Se.

However, Jung later published a much shorter pamphlet on his personality types called "A Psychological Theory of Types" (1931). The full text does not seem to be online anywhere except on Google Books. In it, Jung describes some concepts that are very important for socionics. He realizes the importance of the "compass" of personality, which has Intuition, Feeling, Sensing, and Thinking at its four corners, each function across from its opposite. In socionics this forms what we would call a supervision ring or benefit ring, since each of the leading functions of the types in the ring must correspond to these four categories.

"The four functions are somewhat like the four points of the compass; they are just as arbitrary and just as indispensable.

Nothing prevents our shifting the cardinal points as many degrees as we like in one direction or the other, or giving them different names.

It is merely a question of convention and intelligibility.

But one thing I must confess: I would not for anything dispense with this compass on my psychological voyages of discovery. This is not merely for the obvious, all-too-human reason that everyone is in love with his own ideas. I value the type theory for the objective reason that it provides a system of comparison and orientation which makes possible something that has long been lacking, a critical psychology."

Instead of "critical psychology" we may say: a mathematical, structural theory of the self.

This compass is the crux behind socionics and indeed reality itself. Although it may seem attractive, any attempt to found socionics purely based on dichotomies (and in ignorance of the relationship group) seems to me doomed to fail. That is because it does not acknowledge the geometric transition between discrete traits that is given by the continuous rotation of the square.

----

Jung says regarding psychiatry: "Its concepts are lacking, facts are not; on the contrary, we are surrounded—almost buried—by facts."

This is exactly the situation we still find ourselves in with socionics. While of course it would be desirable to have a way to mechanistically ("empirically") verify the facts of socionics, this is not within the realm of possibility at the moment. What we need now is conceptual clarity and rigorous definitions.

Jung also offers some prescient definitions:

"Just as extraverted sensation strives to reach the highest pitch of actuality, because only thus can the appearance of a complete life be created, so intuition tries to encompass the greatest possibilities, since only through the awareness of possibilities is intuition fully satisfied."

"Sensation establishes what is actually present....intuition points to possibilities as to whence it came and whither it is going in a given situation." 

This is in fact exactly how I see sensing and intuition in socionics - actuality vs. possibility, or presence vs. absence. It's something that perhaps got lost in the formulation of socionics.

However, Jung defines thinking as "meaning" and feeling as "value" which is far less clear.

Quantum Socionics

Around six years ago, I embarked on a project to discover the true essence of the information elements. It seemed to me that their descriptions were either, on the one hand, a collection of disjointed concepts ("essence, potential, possibility, talent, etc") or overly vague and abstract, unconnected to the practical experience of the elements ("internal statics of objects"). My reasoning was that, if for example Se essentially conflicts with Si, then the two must each have some essential quality that is responsible for this — the collection of traits otherwise seems like some kind of fluke or coincidence.

Although I have made considerable progress towards this goal, and I still expect to find a true system of definitions, it seems to me now that the original goal has to be modified slightly. Socionics has certain aspects, both formal and conceptual, that relate to quantum mechanics. In quantum mechanics you cannot assign all properties of a system (such as momentum and position) simultaneously: once you measure one aspect, your choice of what to measure makes the other properties somehow ill-defined or nebulous. This may also be the case in socionics, for example: from the point of view of Te, Ti is about simplifying, ignoring, or reducing information. But from an Fe point of view Ti is more about clarity and organization. These incompatible points of view are what result in quadra values, and compatibility and conflict.

This suggests that information elements must be defined at some level by their interactions. Normally definitions assume some pre-existing framework, and use language to specify some class or individual within that framework. This is the Ti approach. But in a more fundamental theory this may not be possible: if the IM elements are themselves prior to any information, how can they be specified? This is a paradox, and its resolution requires incorporating the dynamic Fe perspective as well.

In fact, information (literally "putting into form") itself is only made possible through an interacting complex of entities. Where there is no distinction between here and there, self and other, there is no transfer (nor anything to transfer) and therefore no information. Geometry and information are two sides of the same coin.