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Thread: Intertype Relationship Diagrams (Math)

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    Default Intertype Relationship Diagrams (Math)

    This is the result of looking into the group properties of the intertype relations.

    Please be selective if you quote the OP.

    This is a good resource if these pictures look interesting but you're not sure what it quite is:
    https://en.wikipedia.org/wiki/List_of_small_groups







    Last edited by Lao Tzunami; 08-01-2018 at 09:46 PM.

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    And whats the point in these visualizations? I think the table is a lot more readable and informal and the graphics is difficult if sometimes impossible to read and doesnt bring anything new to the table. Also if it needs to be visualized, you could choose simpler forms.

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    Quote Originally Posted by falsehope View Post
    And whats the point in these visualizations? I think the table is a lot more readable and informal and the graphics is difficult if sometimes impossible to read...
    Are you saying more people would understand subgroup homomorphism and closure if I wrote them formally as proofs?


    Quote Originally Posted by falsehope View Post
    ... if it needs to be visualized, you could choose simpler forms.
    Cayley graphs, cycle graphs, and finite projective geometry are the only ways I know of visualizing abstract groups, but if you know a simpler way, I'm all ears.
    Last edited by Lao Tzunami; 08-02-2018 at 12:01 AM.

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    sensing tells you an object is there and thinking tells you what it is [1]... I think this a good way of demonstrating their general purpose, which is not so much teach or progress toward some specific goal, but simply represent something they have an intuitive perception of, if for no other reason than to establish its reality. for them producing an object is more like art for its own sake, its enough to give it form, its not about the work such an object does except within that limited scope, hence the questions about what does this really shows us and so forth are beside the point. it shows us something is there! its an introduction, so to speak, now be polite







    [1] I left out this is all in a 2d/2d context, and needs to be looked at that way

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    sorry it wasn't directed to you in particular, because I thought you were rude (you're not), it was just more that Fe is oriented to polite relations, and it sort of like "cool, let me sit down and have a look at this thing--see if I can make some sense of it" which is like the Ti/Fe expectation for interaction. If the relationship takes on the character you could see how both sides might feel positively about the situation and so forth, SLE (for the sake of argument) might be able to extract useful information they were unaware of before and so on. everyone who meets this sort of thing with "what's the point of this" immediately loses out, ironically. even if one doesn't see the point its sort of like a general commitment to politness sort of "starts" one down the road to maybe getting some and so on

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    Quote Originally Posted by crAck View Post
    Offtopic: What's with IEIs and having such visual thinking? Is this all IEI (exaggeration), or just something I've coincidentally noticed?
    I know IEIs are often artistic. I've only met one other IEI who was good at math, and I'm not sure if he understood things visually.

    I really like platonic forms. All I'm trying to do here is draw every part of socionics that we understand until I can see the whole thing for what it really is - the true form of socionics. I'm annoyed that everyone keeps on making all these different models. If we're going to be fancy, we should go to the core of what socionics "is", prove those part scientifically, and then have 1 overall model that everyone can agree on.
    Last edited by Lao Tzunami; 08-02-2018 at 04:19 PM.

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    Last edited by Lao Tzunami; 10-06-2018 at 06:00 PM.

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    Last edited by Lao Tzunami; 10-06-2018 at 06:02 PM.

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    OK. It is quite fascinating that people like to visualize things like that. To me it is usually more confusing to think in rotatable figures. This time connective pointy arrows actually starts to overlap with my thinking.
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    I tend to be suspicious of symmetrical linear representations of human interaction, especially when there's a fair amount of debate over the definitions of the information elements, which, for math, should be clearly defined independent variables. These charts remind me of some proposals where old ideas are made to look impressive - as if new insights have been found..........

    a.k.a. I/O

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    Quote Originally Posted by ajsindri View Post


    I think probably ∘ or * should be used instead of + here; + usually implies that the operation is commutative.

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    Quote Originally Posted by thehotelambush View Post
    I think probably ∘ or * should be used instead of + here; + usually implies that the operation is commutative.
    I was thinking '+' in terms of concatenation, but I'm happy to change it if you think it is best. The relations are group actions, correct? I noticed in your article, you used a dot operation. Is that the standard, non functional notation of a group action?

    Quote Originally Posted by Rebelondeck View Post
    I tend to be suspicious of symmetrical linear representations of human interaction...
    You realize socionics is base entirely on a symmetrical linear representations of human interaction, right?

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    Quote Originally Posted by ajsindri View Post
    I was thinking '+' in terms of concatenation, but I'm happy to change it if you think it is best. The relations are group actions, correct? I noticed in your article, you used a dot operation. Is that the standard, non functional notation of a group action?
    Dot also works - anything but +

    The relationships are group elements.

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    So if I wanted to understand these, what would I need to know?
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    Quote Originally Posted by ajsindri View Post
    .......You realize socionics is base entirely on a symmetrical linear representations of human interaction, right?
    That's likely part of Socionics' problem. Feedback loops, which I'm sure are present in these information control systems, do create a certain amount of non-linearity.....

    a.k.a. I/O

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    Quote Originally Posted by golden View Post
    So if I wanted to understand these, what would I need to know?
    Some basic group theory. I tried to explain the basics in as simple terms as possible here, if you're interested.

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    Also, @ajsindri, there should probably be some indication also that "Reinin relationships" are Democracy/Aristocracy preserving while "Tencer relationships" are Rationality preserving.

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    Quote Originally Posted by thehotelambush View Post
    Dot also works - anything but +

    The relationships are group elements.
    Ok, should be fixed. Thanks for pointing it out.

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    Quote Originally Posted by Rebelondeck View Post
    That's likely part of Socionics' problem. Feedback loops, which I'm sure are present in these information control systems, do create a certain amount of non-linearity.....
    I'm not sure what you mean by "symmetrical linear representations." "Linear representation" has a formal mathematical meaning that does apply to socionics, which doesn't contradict the fact that the rotations (order 4 relationships) give circular loops (the benefit and supervision loops).

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    Quote Originally Posted by golden View Post
    So if I wanted to understand these, what would I need to know?
    You just need to understand Model A. It might help to imagine specific types.


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    Quote Originally Posted by ajsindri View Post
    You just need to understand Model A. It might help to imagine specific types.

    Yes, that helps, thank you.
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    Quote Originally Posted by thehotelambush View Post
    I'm not sure what you mean by "symmetrical linear representations.".......
    For example, the Ti-set of an ESE doesn't map one-for-one into the Ti of a LII; there can only be, at best, a partial mapping but processing priorities will likely obscure most of that. The arrows themselves must be nonuniform because information transformations will likely depend on type pairings - and mapping one way won't be the same as in the opposite direction.......

    a.k.a. I/O

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    Quote Originally Posted by Rebelondeck View Post
    For example, the Ti-set of an ESE doesn't map one-for-one into the Ti of a LII; there can only be, at best, a partial mapping but processing priorities will likely obscure most of that. The arrows themselves must be nonuniform because information transformations will likely depend on type pairings - and mapping one way won't be the same as in the opposite direction.......

    a.k.a. I/O
    That's an interesting point. Very broadly the types all "have" the same elements, but you're right that they are differentiated in ways not captured explicitly by Model A.

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    Quote Originally Posted by Rebelondeck View Post
    For example, the Ti-set of an ESE doesn't map one-for-one into the Ti of a LII; there can only be, at best, a partial mapping but processing priorities will likely obscure most of that. The arrows themselves must be nonuniform because information transformations will likely depend on type pairings - and mapping one way won't be the same as in the opposite direction...
    Oh is that what you mean? That is already a common understanding in model A. Nobody is saying different types express the information elements the same. Projections from the suggestive function is often a need/ request. In duality, both people's suggestive function projects onto their partner's base, which are easily reciprocated. But in the benefit relation, the benefactor projects their suggestive function onto their beneficiary's vulnerable, which cannot be reciprocated. Over time, this creates a dynamic where the beneficiary is not able to fulfill the needs of their partner, and the benefactor's unfulfilled requests stack up, which is why benefit is also call the intertype relation of 'request' by some schools.

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    @ajsindri The 'math' should be a comprehensive representation of, for example, "the common understanding in Model A" and the diagrams should accurately demonstrate the math - otherwise, diagrams might not be as illuminating as one may think.......

    a.k.a. I/O

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    Quote Originally Posted by Rebelondeck View Post
    @ajsindri The 'math' should be a comprehensive representation of, for example, "the common understanding in Model A" and the diagrams should accurately demonstrate the math...
    Both the math and the intertype relation diagrams show this. If you are insinuating they don't, you don't understand them. That is why the ring relations have two forms.

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    Quote Originally Posted by ajsindri View Post
    Both the math and the intertype relation diagrams show this. If you are insinuating they don't, you don't understand them. That is why the ring relations have two forms.
    You are absolutely right; they don't make sense to me and because I cannot be constructive to this thread, I shouldn't have posted. From my limited understanding, it just seemed as if a hole was being dug deeper.......

    a.k.a. I/O
    Last edited by Rebelondeck; 10-09-2018 at 01:54 PM.

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    Quote Originally Posted by Rebelondeck View Post
    ...they don't make sense to me...
    I'd be happy to explain them to you if you're interested. If you already understand the Model A intertype relations, you are most of the way there.

    As @thehotelambush mentioned, they are colored blue if the two types share rationality, red if they share demo/aristocracy, grey if they share process/result, or black if they share all three.
    Last edited by Lao Tzunami; 10-13-2018 at 05:55 AM.

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    Quote Originally Posted by ajsindri View Post
    I'd be happy to explain them to you if you're interested.......
    Thank you for your offer but I think that I understand; it just doesn't make much sense to this old systems engineer. Socionics sits at the interface between brain mechanics and cognitive activity; I think that this interface can be better represented by information control-system models rather than these classification structures that seem based on disputed empirical data - and mathematics won't improve faulty models......

    a.k.a. I/O
    Last edited by Rebelondeck; 10-13-2018 at 02:05 PM.

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