Coordinates and Disagreement

Let's talk about 'A': a random thing right off your mind.

Figure 1: 'I like A!'

Sometimes we say 'I like A', but what we mean is 'I don't like B'. Or in system made up of A and B, A exhibits more positive value to me than B does.

Figure 2: 'I don't like A!'

At another time we may also say 'I don't like A' but in fact we mean 'I like C'. Or in a system made up of A and C, C exhibits more value to me than A does.

The fact that A present in the two scenarios above implies that A refers to a multidimensional object in a global space. At the onset of a conversation, we may only refer to a subspace (to be referred as communication space).

Let's say objects named A, B and C all have the intrinsic* properties x and y (e.g. apple, banana, orange have the properties sweetness and sourness).

*the word intrinsic should not be taken too seriously.

Figure 3: identity space

Also, there are person X and person Y (e.g. human) who have the exact same value (e.g. taste) for A, B, C (denoted as values on z axis) in the global space (to be referred to as identity space).

Now if at the onset of their conversation, X is in communication space xz (a plane in parallel with xz-plane), Y is in communication space yz (a plane in parallel with yz-plane)*, and they communicate with the messages 'A+' ("I like A!") or 'A-' ("I don't like A!") respectively as their classification of A's relative value in their own communication space (which depends on the slope around A). As a result, even though X and Y completely agree with each other with A's value in identity space, they would appear to be in disagreement.

* Forgive me that the figures are a little confusing. Just understand that in figure 3, AB is in parallel with plane xz and AC is in parallel with plane yz. Anyways, the only purpose of the crude diagram is to make it easier to understand the arguments, and the detail of the diagram per se is not of any importance.

The disagreement may lead to a few interesting consequences. For instance,

1. In the most boring case, the conversation terminates immediately after the first round of message exchange. No value-adjustment is bound to occur. The disagreement leads X and Y, who are both highly confident with their own value system in general, attribute the disagreement to an intrinsic individual difference, i.e. they suppose their identity spaces are very different in nature (e.g. in entirely different coordinate systems).
   
   Here it is better to introduce a parameter, general confidence, to mark one's reaction style* to any perceived disagreement in general (which cannot be faithfully observed in a short period of interaction); and another parameter, special confidence, to mark one's confidence in a specific proposition/message (e.g contingent on how steep the slope of AB is)**.
   
   * More specifically, one's general tendency to preserve an initial value (a general inertia--a more intuitive name to myself).
   ** The above-mentioned 'message' can be considered the product of a lossy representation of the original AB relationship in X's communication space. The loss of information (through the transformation of a real number, i.e. the slope, into a dichotomy, i.e. +/-) would then be translated into X's confidence (or certainty if you wish) of the message.
    
2. In some slightly more interesting cases, the conversation terminates but at least one of X and Y ends up adjusting his/her value of A (e.g. X changes his/her slope of AB, thereby changes his special confidence of the message 'A+')*.
   
   * as you might have noticed, I assume that messages are sent and received only in one's communication space, but changes have to happen in the identity space.
   
   One may heuristically describe it as: either X is influenced by Y or Y is influenced by X. By using this description, we subject ourselves to the illusion that it is a processes of special confidence transfer or value transfer, e.g. X has drawn Y's value of A towards X, if Y's general confidence and/or specific confidence is less than those of X. In fact, that can be exactly what Y would imagine if Y has changed his/her own value of A ("X has convinced me!"). We are often inclined (or at least me) to do the mental transformation of my own loss of special confidence into the other person's gain of special confidence, as if it is a currency of some sort.
   
   However, in this scenario there is no causal relationship between X's and Y's change of value/special confidence. The cause of value adjustment is the discrepancy between the messages and one's own general/special confidence. Therefore, it can be that (a) both X and Y increase their value of A ("He's almost an opposite person of me."--imagine a rotated coordinate system); (b) both X and Y decrease their value of A ("Maybe I'm wrong."); (c) one increases his/her value while the other decrease his/her value.
   
   As a result, there would be a 'split' of the identity structure (the relationship between A, B, C in each person's identity space--and remember that X and Y start off with the same identity structure before they have any communication). No matter how X adjust the slope of AB and how Y adjust the slope of AC, since neither X's AC nor Y's AB has been affected, their overall value structure is bound to diverge. Interestingly, even though, for instance, C has never entered X's communication space, the relationship BC is still affected by the communication and might manifest itself through X's future communication with others.
    
3. A more realistic scenario: X and/or Y continue to send more messages to support his/her view. If  A, B, C are the only stuff that have ever existed in X's and Y's lives, either X sending 'B'/'B-' or Y sending 'C'/'C+' would expand the other person's communication space and bring forth his/her supplementary message. Eventually, X's and Y's communication spaces converge to identity space, and the previously perceived disagreement would be resolved. Their value can both be strengthened and there should be no split of identity structure- the miniculture has survived.
    
4. To achieve an agreement (e.g. the scenario discussed in 3), subsequent communication does not have to occur. We can imagine that there is another possible (and more interesting) response to disagreement, other than changing one's own value. For example, X has high general confidence but also very fluid, meaning he/she does not dwell in a particular communication space for very long*. Especially when there seems to be an disagreement, X is very likely to expand or shift his/her original communication space. X would end up agree with Y if the the shifting/expanding communication space of X ends up coincide with the identity space (expanded), or even coincide with Y's communication space (shifted, or first expanded then shrinked). This scenario is more interesting than 3 in the sense that agreement can be asymmetric, e.g. X perceives an agreement, while Y perceives a disagreement.
   
   * In case you are confused, remember that I made up a concept 'general confidence' as the inertia of one's values, i.e. identity structure, while now I just made up another concept 'fluidity' as the inertia of one's communication space per se.
    
5. All the scenarios above are utopian cases created to put forward a minimalistic discussion.  In the most realistic cases, the dimensionality of one's identity space (together with its communication space) can be much higher than three, if not infinite in principle. AB and AC can appear in various communication space and in various orientations/shapes, then it becomes very difficult for X and Y (even they have the same identity structure) to converge their communication space only by shifting. Expanding one's communication space or increasing the number of messages exchanged might increase the chance of convergence but not to a promising degree*. It is interesting that, as the dimensionality goes higher, the progress and outcome of communication becomes dominated by its effect on the location of one's communication space, rather than the identity structure.
   
   * By saying so, I assume that the dimensionality of a communication space is highly constrained, i.e. the dimensionality of the identity space is orders of magnitude higher than that of the highest possible dimensionality of its communication space.
   
   This scenario sounds frustrating: how is it possible at all to communicate? Fortunately (or unfortunately), the primary goal of X for example, as in 4, can simply be to find an agreement with the message 'A-' in his/her own identity structure, and settle. As soon as X's communication space (by shifting/expanding/shrinking) coincides with a space where A exhibit less value than another arbitrary object, no value adjustment or subsequent communication is necessary to occur*. Then the interesting thing about high dimensional identity space is that X and Y can come to an agreement but on very different things**. Therefore agreement does not require the convergence of communication space.
   
   * Nevertheless, in real life, subsequent communication might make X realize that they are not actually in agreement.
   ** As a reminder, all the scenario above are created with the assumption that the messages one send do not completely represent the information in one's communication space, which further does not completely represent the information in one's identity space.
   
   It seems that regarding high dimensional objects, communication can be futile as it tends to generate artificial agreements, e.g. the information that X is referring to with the message 'A+' may never reach Y.  However, it should also be noticed that even in the 3D cases like 1~4, both communication space and identity space are still subjective or relative, which is to say, X's identity space and Y's identity space are isomorphic but separate spaces that can only influence each other through messages.  There is not an absolute space to coordinate the position of X's identity space and Y's identity space. The so-called 'convergence of communication space' is in nature the mutual yet subjective agreement over their isomorphic but separate identity structures. Therefore, the nature of an agreement reached in a 3D scenario may not be quite different from one reached in this higher-dimension scenario.

We can make a more general case by substituting the original interpretation of z (one's personal value/opinion) with another property of A, B, C (e.g. bitterness). Then the above discussion on the communication of subjective value/opinions should still be applicable to the communication of those more 'objective' 'facts'*. We can also insert another axis t for time, then the scenario of communication can also include the discussion of sequences of events. However, I am not proposing this is what the world (physical world or mental world) is like. Those are the assumptions that are useful so far as to help me describe a process that resonates my feeling about communication: a process that is not as straight forward as one could be captured by 'information transfer'. An additional implication can be that you may or may not agree or disagree with a point that I did not make at all.

* In the context of this article, the word doxa/δόξα may resonate.

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Supplementary discussion (a stretch):

A general problem emerges from the above discussion: how X manage to choose messages or symbols that happen to be translated by Y into an isomorphic structures.  It is beyond the scope of this article and my capability to make guesses. Nevertheless, it is conceivable that each person has gone through a long history of communication. Through this history, one does not live in a world where 'A','B','C','+','-' are the only symbols he/she has ever been exposed to -- but rather, one lives in an ocean of messages/symbols from an ocean of sources. Picking up frequent concurrent symbols (or sequences of symbols) help one to locate, then to select message sources. If you are willing to use a more general definition of message (e.g. light waves, sound waves, waves transformed through machines), also a more general definition of message source (i.e. anything that can send out messages of this general kind), you are welcome to think about the A, B, C in the above-mentioned identity structure as essentially the representation of information sources.

Herbert Blumer's words on symbolic interaction may resonate:

 "Human beings act towards things on the basis of the meanings that the things have for them"..."the meaning of such things is derived from, or arises out of, the social interaction that one has with one's fellows"..."these meanings are handled in, and modified through, an interpretative process used by the person in dealing with the things he encounter."(Symbolic Interactionism, 1969)

P.S. Some may find the above article also resonate with Genetic Algorithm (J.H. Holland) (especially the concepts of schemata and intrinsic parallelism) and Cognitive Dissonance (L. Festinger). Feel free to imagine!