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.