1. ## Vectors of Duals

Alright so you can describe a type as a vector, but what vector does your dual take. Specifically if you were to describe arrows and diagrams.

I take it conflictor would be a arrow pointing the exact opposite direction.

Alright so you can describe a type as a vector, but what vector does your dual take. Specifically if you were to describe arrows and diagrams.
Assuming dual elements are 1/4 of each other: y=1/4x

I take it conflictor would be a arrow pointing the exact opposite direction.
I'm not sure. Consider Quasis too.

Alright so you can describe a type as a vector, but what vector does your dual take. Specifically if you were to describe arrows and diagrams.

I take it conflictor would be a arrow pointing the exact opposite direction.
There are others on this board heaps better at maths than me, but...

Playing with vectors! Very loose conceptual terms without getting into the nitty-gritty of the arithmetic or mathematics involved.

First thing, use polar coordinates. The argument of a vector is which type it refers to. All type vectors have a modulus of 1.

Intertypes wind up being summary vectors with modulus √2 and an argument that's an average of the arguments of the two types involved.

This could potentially be useful since you can continue combining vectors for different-sized groups. (And for instance use vectors to explain things like the Block or Square groups.)

I'd have to play around with the details of the maths involved though, and I kind of don't want to or I'll get lost for hours

If you're using a two-dimensional plane (neatest presentation, but may not be "mathematical" if you want to produce elegant and visually meaningful summary vectors), I would organise it so that:

• Each type Quadra occupies a quadrant (going anti-clockwise from the first quadrant, Alpha, Beta, Gamma, Delta)
• Each type is paired with their Activator
• Duals are mirrored through their quadrant's halfway line

This needs work, it's inelegant and produces meaningless results. If anyone else wants to fix up the pieces, by all means.

--

Different approach:

If you're not doing things graphically and instead opt for a numerical approach:

Each type is a four-bit vector. Your starting type (ENTp, for the sake of convention) is <0,0,0,0>. Toggling any of those bits toggles the dichotomy it refers to: <0,0,0,1> would be an ENTj, a quasi-identical.

We however don't have any useful directional words for four-dimensional space. So your question is only really defined in 2- and 3-dimensional space. (You can potentially express 2-dimensional directions in 3 dimensions, as the complex plane "folds up" to form the surface of a sphere, which if I recall correctly is called the extended complex plane or such).

Alright so you can describe a type as a vector, but what vector does your dual take. Specifically if you were to describe arrows and diagrams.

I take it conflictor would be a arrow pointing the exact opposite direction.
I know what you mean, I also try to make some abstract picture of what dual and conflict is. And ofcourse 14 other different 'vectors' or whatever. But it's hard...

16 variants would mean for example, a 2 by 2 block. then 2 arrows that can point in 2 directions. etc. until you have 16 possibilities.

But my brain gets hot when I start thinking further about this, but I like your idea. I hope one day you can solve it for me :-)

5. So I've just thought of this, and my knowledge of vectors is limited to internet research a week ago, but:

First of all, the vectors will start at the origin.
Proximity to mod[y] = mod[x] will denote stability of relationship.
Distance from the origin can represent some form of strength of relationship.

Put the head of the vectors at points (7, 24), (9, 16), (16, 9), (24, 7). NB: They are such numbers because they are equidistant from the origin.
Note that if you add the vectors together, ESFj and INTj will be at point (31, 31), which is on mod[y] = mod[x], and is a fair distance (in terms of both x and y) from the origin. A similar pattern occurs for ENTp and ISFp.

Third (Gamma) Quadrant, the points (-7, -24), (-9, -16), (-16, 9), (-24, -7), then similar intraquadra patterns occur as in the first quadrant. However, the nature of our placing allows conflictors such as ESFj and INTp to add to point (0, 0), a place of very slow strength, according to our definition, although, apparently, much stability (could conflictors be considered to have a very stable state of conflicting?)

I was thinking that INFp could be at point (-7, 24), as this would mean both -dominants would be along line x = -7. However, this implies that the relationship between an INFp and an ESFj brings them to point (0, 48). Being a supervisor relationship, it is not very stable (distance from mod[y] = mod[x]), but it is quite a distance from the origin (indeed, greater than the duals). As such, I would suggest that mod[y-coordinate] (i.e. the distance in terms of y), be a certain aspect of a relationship that a supervisor relationship may have a lot of (chemistry, or something?) and for which I need ideas.

Also, I think we should make the x-coordinates and the y-coordinates actually mean something. That is, for example, we make the y-coordinate "sociability", and so ENFj and ESFj would be on the line y = 24, and ISTp and INTp would be on the line y = -24.

Thoughts?

6. ITT: maths nerds scaring everyone else away.

P.S. I love you, that's awesome.

7. I like math, but even I would never think of this.

I'm not sure this is entirely necessary, or useful.

Maybe it would be possible, though... of course, the values would be more or less completely arbitrary.

EDIT: It would be possible using three-dimensional space, I think. Having three axes would divide the continuum into octants. From there, one axis could indicate introvert-extrovert, another intuition-sensing, and the last logic-ethics. Then all that's left is rational-irrational, which would obviously have to use something other than an axis. Four-dimensional space is more or less completely unworkable. The difference would have to be made in the graphing of the function itself.

Duals would be perpendicular vectors, I think.

EDIT2: I would rather the rational-irrational be exchanged with introvert-extrovert. It just seems to work better that way. Perhaps Introvert vectors can be dotted and Extrovert vectors solid?

8. The dual is the polar opposite.. hence the word dual.

This is what a graph of duality looks like:

9. Originally Posted by nil
I'm not sure this is entirely necessary, or useful.

Maybe it would be possible, though... of course, the values would be more or less completely arbitrary.

EDIT: It would be possible using three-dimensional space, I think. Having three axes would divide the continuum into octants.

Duals would be perpendicular vectors, I think.

EDIT2: I would rather the rational-irrational be exchanged with introvert-extrovert. It just seems to work better that way. Perhaps Introvert vectors can be dotted and Extrovert vectors solid?
I doubt this would ever be useful, mainly because we'd have to edit the system according to what Socionics governs, and it's far too abstract to have much grounding in what actually happens between people. However, it's still interesting to see what happens. I think if we end up with anything coherent, it will have to be a representation of the system, and not anything from which we can learn something new

If we do use a 3D space, then I would agree with the use of a rational-irrational as an axis, in order for us to get a perpendicular vector, and to avoid conflictors and duals occupying the same space. The problem is, however, conflictors and activators occupy the same space.

Maybe something like (1, 1, 1), (perceiving, intuition, thinking) and (1, -1, -1) (perceiving, intuition, feeling). Does that make them perpendicular? 3D space gets more difficult conceptually.

Or could we even use the Reinin Dichotomies as the axes?

The dual is the polar opposite.. hence the word dual.

This is what a graph of duality looks like:
*Graph*
Ooh, new hobby, associating graphs with Socionics relations. An interesting concept, and not to nitpick, but how would Conflictors look? And so and so forth, I think the problem is that I feel that using y = 1/x is too boring for my .

11. Well if y=1/x is duality, you have there a basis for graphing the functions, since they're built on duality. You'd just have to add complexity to it. But I'm not sure y=1/x is the perfect equation for duality yet. I think x^2 and √y would be closer to 2 simple dual functions. The exponents are more fundamental operations than multiplication / division. And that's pretty much just a fractal vs. whatever the opposite of a fractal is. Expanding square thing.

The dual is the polar opposite.. hence the word dual.
Don't be mixing up dual with duel.

Dual: "composed of two usually like or complementary parts"

Alright so you can describe a type as a vector, but what vector does your dual take. Specifically if you were to describe arrows and diagrams.

I take it conflictor would be a arrow pointing the exact opposite direction.
I always imagined duality as two magnets attracting and repelling in a continuous loop.

First they are attracted then issues come up and they are repelled because of their faulty perceptions, they both grow from the experience and perceptions are corrected and they are again attracted and the cycle continues til they die.

14. As I can see there is very little use, mainly because if we try to turn the system into some maths form, it'll just abstract it. So we could never use it to actually learn anything about the types or the people, but you could use it as a (albeit unnecessarily complex) representation of some Socionics, but I don't think there is a use.

That being said, the idea behind the post was to take the idea of Vectors and Intertype Relations and combine them, which I thought was interesting. Perhaps, unless people think otherwise, we could move it to Anything Goes.

15. Originally Posted by Timmy
Don't be mixing up dual with duel.

Dual: "composed of two usually like or complementary parts"
well opposites are always alike, aren't they jackass? The two lines on the graph are alike - they're defined by the same coordinate system and they're directly related to one another through the equation. Fucking dipshit

16. Why are you so mad, Crazed?

I thought this picture accurately depicted duality the first time I saw it:

There is movement, by the way.

17. Originally Posted by nil
I thought this picture accurately depicted duality the first time I saw it:
no this reminds me of a snake doing fellatio to himselve

18. It depends on what coordinates you choose. For example, when using four Jungian dichotomies, you'll get conflictors as the exact opposites. If that's what you mean, duals' vectors would differ in all dimensions except for one. However, if you chose Reinin dichotomies of Static/Dynamic, Strategic/Tactical, Positivist/Negativist and Asking/Declaring, duals would be represented by vectors with exactly opposing directions.

19. Originally Posted by Jarno
no this reminds me of a snake doing fellatio to himselve

20. It's kind of explains you are so bad at socionics when you can't even get the principles of duality right.

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