Discrete & Continuous (S/N) Computational Definitions

[Juan E. Sandoval]

Hello!
So I've recently completed a first draft of the codes for M+ (Ne), M- (Si), V+ (Se) and V- (Ni). You can find these codes on the Wiki right now, but they'll probably require more explanation before they make sense, which is what I hope to accomplish in this thread.
Having already coded P+ and P- before, the first order of business is codifying the discrete ("S") and continuous ("N") processes involves defining what S/N mean from a mathematical point of view - which is what I hope to outline below.

N as intersectionality

I looked to the work done by mathematicians in set theory for a method of formalizing this category. In general, sets theory deals with collections of objects, and the intersections among the sets. The most basic form of this is the venn diagram:

Here, there is a set of objects "A", and a set of objects "B". The overlap between the two object sets is called "A ∩ B." The symbol "∩" denotes the intersecting area. The areas not within the intersection also have a name, and are called the "difference" and is denoted by the symbol: Δ. The combination of the intersection and difference is called the union and is denoted by "∪". For more information, a basic overview is here.
Now, since we are using a computational metaphor for this, what matters to us most is having a way to model this numerically, such as by:

^ Here we see two matrixes of numbers, and a graphic representation of an overlapping section containing the numbers "22, 44, 91, 35, 62, 67." This subset of 6 numbers would be considered the "intersection" of the two. All the numbers outside of these six would be considered the difference. There are a lot of coding solutions already in existence for looking to check whether two arrays share a set of values -- and that is what I will be using of the codes to follow.
Now, after thousands of cycles and higher abstraction, these numbers above eventually come to represent sophisticated conceptual objects, for example in a venn diagram like so:

^ as you can see here, mammals and fish share an overlap of features ("intersections"), while each having distinct features not shared by the other ("difference").
We use this concept as a way to model N/S, where N is the intersection and S is the difference. However, in practice the entire union of both is present in all objects, such that all objects have discrete realities to them and also overlaps with other object sets. The differences between M and V processing relate to how these intersections and differences are computed. In upcoming threads I'll be outlining how this plays out within the four P functions, but first a few notes...

Ontological Status

As with all aspects of cognition, each object form contains an implicit ontological bias. In the case of continuous (intersectional/N) versus discrete (difference/S) object forms, a person can treat either one with more "reality" than another, depending on what point is being highlighted at any given moment in time. I'm not talking about cognitive types here, but just the concepts in themselves.
For example, if we take the case of dogs and wolves, we can make a venn diagram:

We can then examine the simplified statement: "Dogs are wolves."
This statement, "dogs are wolves" highlights the intersection as having the most defining status, while depreciating the difference. The continuous view takes the fact of the overlap as a means by which to equate the two things. Oppositely, the discrete view takes the fact of the lacking overlap to distinguish the two things.
It's worth noting that both of these views are missing part of the picture -- and the simplifications that either would like to make, are missing out the ontology of the other side. It's incorrect to say dogs are wolves or that dogs are not wolves - since they both are and are not, depending on what is meant.
While we're at it, we can take a more fun comparison using CT itself and Jung/MBTI.

Those who wish to highlight the intersection as the most important aspect (ontologically) may experience no problem with the phrase "CT is MBTI" or even to equate all other typology systems loosely intersecting Jungian work, in any capacity, as the same. Oppositely, those who wish to highlight the differences may be inclined to point out that each of these systems is distinct, and they cannot be equated with each other. Neither of these two positions can properly capture the reality of the situation since -- as with all these dichotomies of ontological status -- they miss out on half the reality if they try to side with one angle only.

Simultaneous Views

Having said that, I actually believe that the most natural perception of objects by most people is to simultaneously register their continuity (N) and their discretion (S) -- depending on whether we're talking about its real-time reality (Pe) or its precedent (Pi). An Se-Ni user may simultaneously see that an object is discretely present in front of them, yet also belonging to a long thematic web in their precedent. Our brains do parallel processing like this, across the four energetic modules, so that we can see both sides together. Still, there may indeed be a tendency to view objects more from one framing than the other, and this can have typological origins - especially in people with standard development.
But the choice of which side to view an object through can also be a matter of paradigm. For example if we wished to distance CT from MBTI, for "PR" reasons or what-have-you, we might choose to highlight the differences from it, as a way to avoid any undesired effects from affiliation. Oppositely, if we wish to associate with MBTI, perhaps for the sake of having a broader social reach, we might choose to highlight the intersections. Due to how either side can be justified on its own, coming down hard on one side may have more to do with how a person wants to frame the information --- under whatever personal motivations they may have.

• This topic was modified 5 years, 2 months ago by Juan E. Sandoval.

[a.k.a.Janie]

Good way to break things down.
I personally wonder why I have a tendency to fixate on the overlap between categories, looking for how things are the same, perhaps at a deeper level than surface appearances suggest. Yet I am "S" over "N" dominant. Maybe it's more of an ego fixation, or something like that, or is higher-level mental stuff than functions/type.
The usage here of the terms "discrete" vs. "continuous" will take some getting used to. Here, "discrete" refers to S and "continuous" to N. Whereas, when I've applied these terms to typology before, I thought of the Se-Ni axis / V+/- as "continuous" and Ne/Si / M+/- as "discrete", but I can get used to this way. I tended to like "concrete" for S and "abstract" for N, but perhaps that's is overly simplistic or inaccurate, as I got it from my first foray into MBTI long ago.

[Juan E. Sandoval]

@janie - oh, I should have emphasized this more in the post, but I wouldn't use this for determining "S" over "N" priority, since this is not how this distinction is meant to be applied. Discrete and continuous are features of certain functions, rather than a dichotomy on their own. These terms help set foundational terms from which to build up descriptions of Si, Ni, Ne, Se - which are what matter. But these terms (D, C) can't really stand on their own two feet as a type-dichotomy.
For example, you're correct to say that Se/Ni in general is more continuous, holistically. But this is due to Ni (V-) having the property of Geometric Convergence. This makes it so that Se/Ni users will generally tend to see how all things interweave into one in the end, independent of whether they treat the present moment discretely. Oppositely, you're correct to say that Ne/Si in general is more discontinuous in worldview, independent of whether they're intersecting objects on the fly at any specific moment. This is due to its Discrete Linear Chronology, which chunks instances into standalone bits, which have a discontinuity across time, making Si/Ne's reality more of a cake of stacked layers.
So if a person is high-Ne, they'll still tend to see reality more as 'chunked' apart, because their 'continuous' and 'intersecting' property is only happening in real-time, while their holistic temporal understanding is discrete. You need a meta-view of both poles of an axes, to really differentiate people typologically into one group or the other. So it isn't S vs N, it's one version of S/N versus another version of S/N.
This is just one example of why the OP's categories are not very useful as a standalone typological dichotomy grouping -- and CT doesn't really do 1-letter-based groupings anyway. And as you know, the computational metaphor notation makes no distinction regarding which function in a pole is atop of the other, so for instance an FiSe =R (Fi-Te as a whole) > V (Ni-Se as a whole) + "-", or (Rv-).
~
I hope I didn't cause greater confusion! No need to reprogram your prior understanding of the functions, haha! You got it right. It's just that this thread isn't referring to individual type aspects. 🙂 There are some differences in function hierarchy in types, but they're not at this level of resolution.

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