# Thread: Functions: Xi vs. Xe

1. Originally Posted by dissonance
It seems like it doesn't make sense to think of the eight functions as entirely separate. Fe and Fi have overlap, Ti/Te, Ni/Ne, Si/Se.

So I propose that there are only four functions (not that this is completely new or anything). Thinking, Feeling, Sensing, and Intuition. There is a spectrum of Introversion to Extroversion for each function. It should not be thought of as binary.

In most cases, people significantly prefer one direction for each function, but there's no reason this should be true in all cases. It does make sense to me that Introversion in one P function leads to Extroversion in the other (same for J functions). But it's never going to be 100% Ni/0% Ne and 100% Se/0% Si. Thinking of Ne and Ni as separate ideas just seems misleading to me (true for all functions).
No..., they do not overlap. Jung says that they are clearly different. In fact Te has more in common with Se and Fe than Ti, Ne and Se are common, but not Ne and Ni and so on. Although they share the same judging perceiving title, Jung states a distinct difference of the functions based on the attitudes (E/I).

2. One Te and one Ti can both output "false". Therefore there is overlap. There is no overlap between N, S, T, and F.

3. Originally Posted by dissonance
One Te and one Ti can both output "false". Therefore there is overlap. There is no overlap between N, S, T, and F.
Te (like all extraverted functions) outputs or decides based on the objective whereas Ti (like all introverted functions) inputs or decides on the subjective. Here is an excerpt from Jung:
There is also, however -- and now I come to the question of the introverted intellect -- an entirely different kind of thinking, to which the term I "thinking" can hardly be denied: it is a kind that is neither orientated by the immediate objective experience nor is it concerned with general and objectively derived ideas. I reach this other kind of thinking in the following way. When my thoughts are engaged with a concrete object or general idea in such a way that the course of my thinking eventually leads me back again to my object, this intellectual process is not the only psychic proceeding taking place in me at the moment. I will disregard all those possible sensations and feelings which become noticeable as a more or less disturbing accompaniment to my train of thought, merely emphasizing the fact that this very thinking process which proceeds from objective data and strives again towards the object stands also in a constant relation to the subject. This relation is a condition sine qua non, without which no think- [p. 431] ing process whatsoever could take place. Even though my thinking process is directed, as far as possible, towards objective data, nevertheless it is my subjective process, and it can neither escape the subjective admixture nor yet dispense with it. Although I try my utmost to give a completely objective direction to my train of thought, even then I cannot exclude the parallel subjective process with its all-embracing participation, without extinguishing the very spark of life from my thought. This parallel subjective process has a natural tendency, only relatively avoidable, to subjectify objective facts, i.e. to assimilate them to the subject.
I am not saying there is an overlap between the extraverted functions, but merely that they can have as much if not more similarity with one another than their introverted counterparts.

4. Originally Posted by Delphyne
Maybe she´s ESFJ.
*high fives for compromise!*

5. Originally Posted by ygolo
Well, in theory a 3-D ellipsoid has 8 degrees of freedom (3 degrees for the origin, two degrees of freedom for the three axis, and 3 for the length, width, height along those axis). 8 degrees of freedom,8 functions--seems plausible.

I was actually trying to think through the equations of projections of the ellipsoid on the various "plane vectors" representing function scores.

Any 3-D ellipsoid can be specified by a 3x3 positive definite matrix, B, (defines axis and "lengths" along those axes), and a 3-D vector, r, (defines the origin).

The bounds of the ellipsoid are defined by the solutions to the equation:

[(x-r)^T][B^-1](x-r)=1

Each cognitive function vector would have a 3x3 projection matrix, P, of rank 1. These matrices are symmetric and have the property that P^2=P.

Now the projection of the solutions to the equation above using P becomes the solutions to:
[(y-Pr)^T]P[B^-1](y-Pr)=1

I was thinking that I could make the function score of the ellipsoid to be given by the maximum valued solution to (8 versions of) the above equation.

For convenience, lets denote the Projection Matrix by the actual function name.

Si score = max y such that, [(y-Sir)^T]Si[B^-1](y-Sir)=1
Ni score = max y such that, [(y-Nir)^T]Ni[B^-1](y-Nir)=1
Se score = max y such that, [(y-Ser)^T]Si[B^-1](y-Ser)=1
Ne score = max y such that, [(y-Ner)^T]Ni[B^-1](y-Ner)=1
Fi score = max y such that, [(y-Fir)^T]Si[B^-1](y-Fir)=1
Ti score = max y such that, [(y-Tir)^T]Ni[B^-1](y-Tir)=1
Fe score = max y such that, [(y-Fer)^T]Si[B^-1](y-Fer)=1
Te score = max y such that, [(y-Ter)^T]Ni[B^-1](y-Ter)=1

Note: in all the above equations the "y" is independently bound, that is, each y is a different y (I just didn't want to do y_Si, y_Ni, etc.).

Other things to note:
-The directions of the axes of the ellipsoid are given by the eigenvectors of B, and the "half-axis length" along those axes is given by the square-root of the corresponding eigenvalues.
-B must be positive definite, and because of that, it must be symmetric (we're dealing completely with real-numbers here).

With the things noted above, we've now created a framework of 9 scalar variables.

--b1 b2 b3
B=b2 b4 b5
--b3 b5 b6

--r1
r=r2
--r3

Given the eight constraints above and one more for positive definiteness, it seemed like it was doable.

The issue is that I haven't yet thought thought what vectors should represent the functions, and I need to make sure that equations given from the projections are independent (or at least not contradictory).

Your 8 functions should be bound by 4 pairs. they can't be independently bound...

for instance: Si score = Max Y so that Ysi = 1 - Yni and Ne score = max Y so that Yni = 1-Ysi.

crap im late for an appointment. will get back to you on the rest of this later...

So much needs fixed. So much...
And then I think to myself that I don't care. Or something like that.
Even though I do.

Ever just run out of energy?

Well anyway, then I saw this.
Originally Posted by ygolo
I am kind-of thinking about cognition as a shape (I'm thinking elipsoid right now) in a three dimensional space, where the cognitive functions become projections on to some vectors (I am thinking 45-degrees into their respective quatrants in the "judgement plane" or "perception plane"). The percpetions and judgement planes as joined along the E-I axis.

Here is a potential elipsoid (and there are man potential ones for a given type) for an ESTP:

Need to cogitate on this some more. I wonder is I can mathematically prove that a 3D-elipsoid can account for all possible scores on the congitive functions test. Seems plausible... need more cogitating.
Ygolo deserves respect.
He's at least on the right track.
I'm telling you dudes... there's shit that each function has in common. Before you can really generalize I and E, you're gonna have to figure out...
Hmm you can't really do that.

Introversion is like having an internal standard of how shit needs to be, and extroversion is having no standard, but just employing what's available to you by "The world" I know that's what everyone likes to say "the external world" like there's two different worlds... Where do these fuckers get these ideas anyway?
Like they're separate or something. Where did that idea even come from?
Like Te prefers to measure things in inches. Ti doesn't care about that. Just as long as it fits. Ti will make Pe 'eyeball it' and make sure it fits. Excusing that, Ti doesn't even measure. In fact, measurement is only an external thing. After all, Pe is the thing measuring it for Ti. Ti just gives confirmation of whether or not it's appropriate. But it's still involving 'the world' right? What's there to decide on if not the world?
What's to measure in inches by Te, if not the accurate size for the chair in the ESTJ's den? Sensory ideal. The ideal says to Te "yes 15 is appropriate" and etc.

Just take that formula down the line.
If it doesn't work then get a book or something I can't figure out how to explain it anymore.

I don't even think the point of this site is to discuss MBTI.
That's a joke. It's far too complicated and not everyone agrees (even though, I'm actually the one who's right) so no real learning can go on. Plus no one really tries.
Yes, socializing. More about jokes and veiled trolling. Good work so far everyone .

I couldnt' stay away.

And if you're curious, don't bother asking. I'm not even sure if I'm being sarcastic.
But I am right.

7. I'm beginning to think I'm too stupid for this forum.

8. Originally Posted by Modern Nomad
Your 8 functions should be bound by 4 pairs.
You are right. That does seem to make things simpler than little nudges to the function
vectors or using “antiprojectors.”
Let introduce a proper coordinate system so that the words “max” and “min” make sense.
We take the S-N axis be the first dimension with S positive.
We take the F-T axis be the second dimension with F positive.
We take the E-I axis be the third dimension with E positive.

9. ## getting the scores from the ellipsoid

We can get the scores from the ellipsoid, like this I think:

Now, I need to eat, but then I can work on getting the ellipsoid from the scores, prving a 1-1 mapping if I am correct. I'm gettting ahead of my self, but perhaps I can make a visualization program to see peoples ellipsoids based on functions....first to eat, and go out w/ friends...probably not till tomorrow with this stuff.

10. ## I was wrong

At least on the purely mathematical mapping, I was wrong.

This is, of course, an over-constraint of the origin. I was thinking with playing with widths, axes, and origin, we’d have enough, but the origin itself is over-constrained.

Unfortunately, it runs into the same problem that many other visualizations I’ve tried. There is a mismatch between extroverted/introverted perception and extroverted/introverted judgment. It seems like we really cannot join the two types of extroversion/introversion. I wonder if this is fundamental, or if there is some trick of visualization I haven’t considered.

So the choices, a “best fit” ellipsoid, using 4-dimension, or a more complex shape (like Modern Nomad suggested).

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