I want to tell everyone what I think about the IEs, so that people can tell me what I have wrong and then explain to me why I'm wrong so that I can be right(er). If you accept that the "internal dyanmics of fields" type descriptions are the very very core of the functions, I'm trying to tease those descriptions out a little bit further, so that we can see how these core attributes lead out towards the generally observable traits. So, I'm not focusing so much on how each element manifests itself. Also, you'll find similarities between each IE description. In general, I tried to define the functions somewhat in terms of each other, so there's similar terms used for both intuitive functions and both sensory functions, etc.
In each IE description, I bolded one or two things that I think are the core of my thought. The rest is really just explanation. Feel free to just read the bolded parts.
My thoughts on the judging functions:
I think that Fe is about how to express emotional states. The second step in Fe is to use those expressions to affect other people's emotional states, first others, then even possibly your own. Fe considers emotional expression and change to be a good in itself. This is why Fe appears to be about LOUD HAPPY SHINY SHINY LOOK THERE OH WAIT I'M SO SAD CRY WITH ME, OH WAIT NOW I'M HAPPY, LOUD LOUD SHINY SHINY LOOK! Of course, Fe is really about freedom of emotional expression and allowing oneself to feel and share that feeling with others. When Fe comes across a sad person, they will modulate their own emotional state in such a way as to ultimately cause the other person to modulate their emotional state (although a person with sophisticated Fe understands that this is not always by doing something exciting and fun; sometimes it's by feeling the way the other person is feeling).
I think that Fi is about how emotional states work in general. The second step in Fi is to formulate actions that take advantage of this knowledge, not via direct emotional expression, but through things like empathy, appearance and social custom. This is why Fi appears to be about behavioral rules and decorum and stuffy delta-ness. Of course, it's really about behaving in ways that will benefit everybody and make people happy. When Fi comes across a sad person, they will use their understanding of emotional situations to empathize and hear the other person out with surprising accuracy.
I think that Te is about how things change in space. The second step in Te is to optimize this movement/change.. Te considers efficiency and doing things in the best way possible to be a good in itself (or at least the most intelligent way to go about things). This is why Te appears to be about boring boring boring, do useless stuff, boring boring. Of course, it's really about how to maximize what you've got, because that's simply the smartest way to go about things. When a Te person encounters a problem, they will take in the facts, and, without coloring them in any way, take a specific action. Te is all about the undifferentiated facts/information, which I think is yucky. I don't understand why Te has an inherently normative character (affecting external states in the best way), but that's the only way I can make it work in my head.
I think that Ti is about how external states work in general. The second step in Ti is to create model of action and then fit actions into that model, as in physics creating laws of motion and then analyzing motion according to these unchanging laws about how things always move. This is why Ti appears to be about hierarchies and rigidity and rules, rules, rules. Of course, it's really about understanding how things work, clearly, precisely, and above all systematically. When a Ti person encounters a problem, they will try to understand the data by fitting it into a system. From the system, a correct action can be deduced, but it always helps to organize the data beforehand, so that one can come to a better understanding of what exactly is going on. (I love Ti. It is crazy helpful. It makes confusing swamps of muck, just information muck, into organized understandable sets of information).
I'm much more confused about the perceiving functions
Ne is internal statics of objects. That means Ne is what is always true about an object internally. I think that this is analogous to Aristotelian essential properties. Like Aristotle, Ne collapses these properties in time. So, for Ne, a seed has the essential properties of the tree it will grow into. This collapsed-in-time aspect is how we get the "possibilities" part of Ne; since Ne sees the acorn as the tree, as having, in potential, all the attributes of the tree, since the essential properties of the seed are the same as the essential properties of the tree, it sees all sorts of different possibilities for the acorn, all the possibilities of the tree: it could have branches, its branches could be thick or thin, it could be flowering, it could be non-flowering, fruit might grow on it, fruit might not grow on it, etc. Ne's focus is not on the actual properties of the completed tree (that's Se). Ne is about the relationship of a thing to its Form.
My favorite analogy for Ni is the one I posted in the what is Ni thread that's up now. If you have a bunch of car parts, Ni is what looks at the parts, comes up with a hypothetical relationship between them, and from that hypothetical relationship, predicts what other parts will be needed. However, the thing about Ni is that I think that it is most notable for the training it gives in abstract thought. Abstraction is the go-to mode for Ni-egos, which is why Ni, especially for betas, is associated with mysticism and the like. Gamma Ni is blocked with Te and thereby tied down to earth. But Beta Ni is blocked with Fe, another thing that requires a degree of abstraction (insofar as we cannot directly know what another person is feeling; we have to guess based on a sort of experience). This results in a function that is very much not tied down. Most of the noticeable head-in-the-clouds qualities IEIs (including Socrates) have result from the fact that our fundamental reality-processing engine is abstract, moreso than how that function actually works. Ni is about how the relationship of a thing to its form changes based on other influences. It can get complicated and think about how multiple relationships of objects to Forms/Ideas change and how these changes affect one another.
Se is external statics of objects. This one is particularly difficult to describe because it is the way of viewing things most opposite to my own (Ni; and if you don't believe me, ask Jung), and I really don't understand it. But it seems to be a way of seeing things that also collapses things down in time (I understand I'm using the language of "collapse" in time because I see things fundamentally from a dynamic perspective), but focuses on the tree, not how the acorn can become the tree. Se looks at a tree and knows what a tree is like, not in terms of its relation to another thing or how it will change over time, but simply in terms of the complete picture given by the senses, especially sight(which is a much more complete picture than it seems like it would be).
Se is like a super-power to me. When I look at something I inevitably do something to it, mentally: I break it down into it's component parts, I look at what is around it and how that affects it, I think about what system its a part of and how that system might work, I think about myself thinking about the object, I think about that myself thinking about the object relates to socionics, etc. But I think that at least part of Se (if not the core of it), is the ability to look at external objects individually, with strong attachment to the sense perception itself rather than anything the mind does to the object. Se types have less of a gap between subject and object because they disregard the gap and just trust the sense perception at a fundamental level, even though they may later intellectually recognize a form of subject-object separation. Se begins with excellence in sense perception, the external relationship of the subject to the object.
Just like many of the properties associated with Ni come not from how the actual process of Ni works but from how the level of abstraction that Ni works at affects an Ni-ego, so many of the properties associated with Se egos doesn't come so much from the actual process of Se as from the consequences of viewing the external world so concretely and certainly. They can make sharp, quick decisions because they live in a fairly certain world, which only becomes uncertain when it comes to guessing how people feel (Fi-polr) or guessing how systems work (Ti-polr). They can act strongly and powerfully because they live 100% in the world rather than in their heads. I wouldn't describe this as "in the moment" because of some of the connotations (acting-based and otherwise) of that phrase, but I would describe it as "in the physical space", firmly grounded in the external objects of sense, etc.
But this description could be 100% off. I really don't know.
Si is external dynamics of fields. Si is how tangible relationships change. Si is how sense perceptions (i.e., the relationship between the subject and object) change based on other influences. How the relation of my eye to the painting changes when another splash of color is added. How the relationsh of my eye to the room changes when a light is turned on. How the relation of my sense-of-touch (sorry, harder to locate in a specific body part than taste or sight) to my back changes when I sit down in this chair. How the relation of my tongue to a sauce changes as I add paprika. That's what Si is concerned with. This leads fairly obviously to understanding how to create something aesthetically pleasing. It can get more complex and consider how several different objects change in relation to several different subjects.