Thinking in "different spaces"
There is a concept known as the "Fourier" transform, which can rewrite a set of equations in an entirely new "space." It is especially useful for any set of equations that results in "wave functions." E.g., sound waves, electromagnetic waves, and so on.
In "real space," the wave equations are complicated partial differential equations, e.g.,
(Sorry this is in mks rather than the more usual cgs units)
In "Fourier space," the wave equations instead become linear, algebraic equations, as shown in some detail in
this link.
In practical terms, the solutions to the "real space" equations is a single, evolving wave form that indicates the specific amplitude at each point in space and time of whatever waves (sound, electromagnetic) the equations describe. If one records a sound digitally, for example in a .wav file, the file records the amplitude of the wave as a function of time, its accuracy dependent upon the number of bits and the frequency of the sampling.
The waves in this wave file don't "look like" the sound at all. It is, rather, the raw data of the sound, the empirical measurement of the values over time.
The Fourier transform shows a different picture of waves. Instead of the amplitude of a single wave, the solution of the transformed function is a
spectrum of frequencies. Some of the frequencies of the spectrum have a low value, others have a high value. Looking at these more closely, these spectra show
notes and
timbre and actually "look like" the sound. A low note has high values at low frequencies, and is almost nothing at high frequencies, and vice versa. A chord is several peaks, each peak a note.
The Fourier space, then, is what we
hear. We don't hear the amplitude as a function of time, but rather, how the frequencies within the overall wave resonate within our ears.
The math is entirely qualitatively different, but describes the same physical phenomena! One is a .wav file, the other is an .mp3 file. Same physics, same sounds, completely different math/numbers.
Which perspective is better? Well, it depends. The "real space" solutions are valuable because they represent values of fields and forces that affect matter. The overall amplitude of a sound wave is important with respect to making sure a microphone doesn't "clip" the peaks. The "Fourier space" solutions are valuable, because they represent the
information contained in the wave: the voice, the notes, the "sounds" as a human would hear them. Given the Fourier transform, it is possible to limit the frequencies one plays back from a recording, e.g., enhancing voice-level frequencies that would otherwise be drowned out by the white noise of wind or the low rumbling of a train passing by.
Thinking in both spaces is useful.
The reason I know a bit too much about this stuff is that I've modeled a plasma by using a combination of these, switching between both spaces. In real space, I would have electric and magnetic fields pushing particles, because in that space, the math is linear algebra. Then I'd take the densities of the particles and transform them into Fourier space. In Fourier space, the math to solve for the fields is simple linear algebra, so I quickly get a solution there. Then I transform that solution back into real space, using the fields I derived in Fourier space, then transformed to real space, to push the particles as I did before. Wash, Rinse, Repeat.
By using both spaces to solve things, I'm able to process the plasma equations much faster than otherwise, with remarkable accuracy. Conceptually, the particles live in real space, and the fields live in Fourier space.
I can use this understanding of real vs Fourier spaces to provide perspective on these endless Fe/Fi threads.
Fe and Fi think in different spaces, Fe-space and Fi-space. Both spaces model the same things, but measure/describe/decipher real events and understandings entirely differently. If you take "Fi-numbers" and put them in "Fe-spaces" without properly transforming them, the Fi-numbers look like nonsense. In fact, they
are nonsense,
in Fe-space. The reverse is true, with raw Fe-data looking like nonsense in Fi-space.
This is entirely the source of differences. What is all-too-often missing is the
Fe-Fi transformation of the raw data. At least one of the two people involved in a conversation has to do the work of the transformation, and it's best if both do it. The "transformation" is, in simple terms, the ability to think in both spaces, that is to say, hear the Fi-raw-data in one's own Fi-space, and the Fe-raw-data in one's own Fe-space. The human brain is quite amazing: if one can switch gears, and listen to others in their own spaces, the transformation to the alternative space isn't that difficult. It's not unlike learning and thinking in a foreign language, or learning to play a new musical instrument: it's not a one-to-one mapping, and it's possible to have entities in one space that simply cannot exist in the other, but mostly it translates over.
I would suggest that while one certainly has one's preferred mode of thinking, it is something of a character flaw to refuse to recognize the
validity of the alternative mode of thinking, especially for communication and interpersonal harmony. That means being able to recognize the alternate mode, and making an effort to understand it in its own terms, before applying one's preferred thinking-space.
Where these threads tend to break down appears to be when a failure to successfully understand/transform the information between thinking-spaces is interpreted as an attack or a willful insistence that information is only properly evaluated in one's preferred thinking space.
Moreover the question isn't
whether Fe vs Fi plays a role in misunderstandings of this nature, but rather
how and
to what degree. People will occasionally misapply or mislabel aspects of these misunderstandings, but that shouldn't be taken as evidence that Fe vs Fi considerations don't apply, but rather should be understood as a failure of understanding in that particular instance.
I suspect that part of the problem is that the Fe-Fi transformation is drastically limited by text communication. Body language, tone of voice, awareness of other contexts only visible to those present in person, all contribute to one's ability to do this transformation. One needs to learn new, text-based, cues to properly transform the understandings, e.g., "if someone is speaking in terms of
how-I-feel, then one should read the words in Fi-space, not in Fe-space."
lol
I'm not really sure what's going on now. 
