It's a very interesting thing, the thoughts between the different functions and how one cannot be a middle user based on such theory.
The thought is that we are seeing things through the abstract categorical system in which one is one over the other by default. I imagine things may be slightly more complex with the given systems and thoughts. If one were to say the example of Fe, Fi, Te and Ti, one would be able to scale them. Each function would use 2-dimensional scales, one of which would be the dichotomy of the F/T and the dichotomy of Introvertion/Extraversion. In essence if it were any other way, functions definitions would simply be random unrelated nodes of judgement or perception which would put the jungian works of the functional models at a dead end. Of course, one would realise it's not such the case with the full understanding of the functions including its scaling factor. If you bring about the example of Ti:
Ti will use the two scales of introversion/extraversion and thinking/feeling where the inclination from the 'unclear' midpoint of both scales would be introversion and thinking respectively. However, from again the unclear midpoint, the issue can be cause of greater confusion as to which is used at the particular time and so one who may be closer to that middle point of the scale, may type themselves as X within the MBTI dichotomies.
Let's take this
example here ^^. The scale from Ti to Te and Ti to Fi bears its strength by what one could use with regards to the lack of strength of the other.
One way is that it could be represented by a sine curve.
The wavelength represents how often a person retracts back to the pure logical mind processes whereas the amplitude represents how much distortion our logical processes are changed by feeling. It of course makes sense that pure logical thought has its impossibility of occurring by a lack of subconscious or conscious motivation to do so, so in essence a feeling is portrayed at all times the sine curve doesn't hit the center axis.
The x axis would represent direction. This would be the dichotomy of introversion to extroversion as purely directional modes of thought towards a particular aspect. Where as one would process the thought with logical construct to application (Te) the other would process the thought with application to logical construct (Ti).
first of all - + 100 rep, i've had a very similar idea years ago when i just learned of the MBTI about representing the midway sections via a wave formation, somewhat inspired by one of the puzzles in Myst... doesn't seem so original now (pfft)... but still from a different direction:
my notion was that the level of extroversion vs. introversion of any given mental process can be described in terms of frequency, defined as the rate of the process relatively to the rate at which we experience it (RoE), and that most differences between an introverted and extroverted function can be defined by that frequency.
imagine a slow motion movie of a water stream: you would be able to see every wave as it breaks against the rocks, every droplet as it flies through the air and arches it's way back to break through the surface of the water. you would catch the patterns within it, learning what will come of each drop like a child learns to figure out where the ball will hit, you would be able to ignore the whole as it waits for you and break down the components of the otherwise chaotic system, as each drop flies the sight of the other drops in similar patterns would still be in your peripheral vision. you sit their in your peace of mind, waiting quietly for the movie to come to you.
now imagine the same movie but in fast motion. the chaotic system becomes even more chaotic, you catch glimpses of what's happening, your trying to figure out the possible variables of how everything was in the moments you missed to figure out the possibilities of where it might go again, you build generalizations to engulf it as a whole without seen what it's made of, your eyes are racing after the stream trying to catch more details, your always experiencing that your missing information so you look to find what others see and as you communicate it you force the view of the stream in your mind to slow down to the rate at which you communicate it.
thus:
when a mental process is moving at a slower frequency then the rate at which we experience it, it is an introverted process.
when a mental process is moving at a faster frequency then the rate at which we experience it, it is an extroverted process.
by illustrating this as frequency, and by calling the Y axis the level of awareness we have of a process, we gain the advantage of a clear visual depiction of for "multiply small glimpses of awareness" as the wave structure crosses the X line at a higher frequency vs. "long focused moments of awareness" as the wave structure crosses the X line at a lower frequency. hopefully the metaphor allows for the entire range between an introverted process and an extroverted process to be immediately and visually apparent.
____________________
i would also add another dimension to the new description, though i am not sure how to represent it on the visual metaphor:
adapting the information to ourselves vs. adapting ourselves to the information.
when we adapt the information to ourselves, we allow it to sink into the schemes and meanings that we recognize at the back of our heads, the patterns and subjective experiences that we intimately know, and process it from in a more Recognizable form. such is the case with intuition and feeling.
when we adapt ourselves towards the information, broken down into the various inputs and tidbits that we have, we experiencing it in it's raw detailed form, making new connections and Generating new mental schemes. such is the case with sensing and thinking.
so a function can be attempting to:
Generate schemes
Recognize schemes
and likewise, can still be perceiving or judgemental.
GP = S, GJ = T
RP = N, RJ = F
whatever way we depict it, it is entirely possible that we are able to do both in the same time, in fact i am pretty sure we almost always have too in order to come up or understand anything at all, so the description here shouldn't present a false dichotonmy but rather a full range of possible gray areas.