Modeling misunderstandings

By Gordon Rugg

Many problems in life are caused by misunderstandings. Misunderstandings take various forms. These forms themselves are, ironically, often misunderstood.

In this article, I’ll look at ways of representing misunderstandings visually, to clarify what is going wrong, and how to fix it.

I’ll use a positive/negative plot to show the different forms of misunderstanding. This lets you locate a given statement in terms of how positive it is, and how negative it is, as in the image below. This format is particularly useful for representing mixed messages, which are an important feature of many misunderstandings. There’s more about versions of this format here and here.

I’ll start with a statement which is moderately positive in some ways, and moderately negative in others. It’s shown in the middle of the plot as a white circle, numbered 1, to show that it’s the first statement. For example, this might represent someone starting to give feedback about a piece of work that has both good points and bad points.

I’m deliberately not showing a particular wording for the statement, to avoid raising questions about whether everyone would agree with that statement really being moderately positive and negative; I’ll discuss the issue of different possible interpretations later in this article.

How can the other person respond to this opening? There are nine main forms of response; eight involve movement, and one involves staying at the same place. These are shown in the diagram below, with arrows for the eight directions.

For example, the other person might react with a statement that is more positive and less negative (moving toward the top left) to send constructive friendly signals, such as expressing gratefulness for the feedback.

Conversely, they might react with a statement that is less positive, and more negative (moving toward the bottom right) in an angry response. In the example below, the second person has gone in this direction, shown by a circle coloured green to show that this is the second person, and numbered 2 to show that this is the second statement in the sequence.

The first person can now respond, either with movement in any of the eight directions, or by staying in the same place as the second statement. For example, in reaction to the second person’s angry negative response, the first person might try to move the conversation back in a positive direction toward the top left, or they might react in an angry negative way that moves further toward the bottom right.

The image below shows some common patterns. The first pattern shows both people moving in an increasingly constructive positive direction. The second shows the second person reacting negatively, followed by the first person sending out a strongly mixed signal, in effect offering a carrot and a stick. The third shows both people moving in an increasingly negative direction; a classic angry escalation.

This format lets us see how interactions can move in different directions. It ties in neatly with concepts such as feedback loops from systems theory and game theory, where a particular action may be amplified or deadened by features of a system (e.g. escalation or de-escalation in politics).

This format also makes it easy to show various forms of misunderstanding.

One classic form of misunderstanding involves ambiguity and polysemy. (I’m using the pair of definitions in which ambiguity involves two separate different interpretations, and polysemy involves more than two; some fields define these terms differently.) These concepts are different from vagueness, which I’ll discuss after ambiguity and polysemy.

A famous example of ambiguity attributed to various wits is: “Thank you for your book; I’ll waste no time reading it”. This has two possible meanings, both of which are clear, but which send completely different signals. One meaning is: “I shall read your book as soon as possible” (implying that reading it is something to anticipate with pleasure). The other meaning is: “Reading your book would be a waste of time”.

We can show these two meanings as two positions in the diagram below. The initial gift of the book is statement 1; the two different intepretations of the response are shown with question marks in the two green circles, to represent the uncertainty about which meaning was actually intended. For polysemy, we would use several such positions, one for each of the possible meanings.

Each of the two meanings above is represented by a single small circle in the diagram, implying that there’s not much doubt about the nature of the signal being sent within each meaning. The positive possible intepretation is clearly positive; the negative one is clearly negative. The key question is about which interpretation is the correct one.

What happens if there’s significant uncertainty about just what a given signal is? This is what vagueness is about. We can show the degree of uncertainty about it via features of the representation, such as the size or shape or colouring of the symbol for the signal.

The image above uses shading to give nuance, and shows possible interpretations on a range from most likely interpretation(darkest) to least likely (lightest). The range of possible interpretations for signal 2 is much broader, and therefore more vague, than for signal 1. Signal 2 is definitely sending out a more positive than signal 1, but how much of a negative signal it’s simultaneously sending out is much less definite.

The key difference between vagueness and ambiguity is brought out by the two images above. With vagueness, you know that the intended meaning is somewhere within a single broad area. With ambiguity, the intended meaning is within one of two separate areas.

In real life situations, ambiguity is usually more dangerous than vagueness, in terms of potential misunderstandings, because ambiguity is very easy to miss; you see an interpretation that makes sense, and immediately proceed in terms of that interpretation, without noticing that there was also a completely different interpretation that also makes sense, but in a very different way. With vagueness, you usually know that a statement is vague, so you’re aware from the outset that there’s the potential for misunderstandings.

Conversely, in some real world situations, vagueness can be a good thing; for example, by offering the other party space for a face-saving way to de-escalate a situation.


This representation makes it easier to see patterns in communication, and to identify where different people are interpreting the same signal in different ways. This can be invaluable for good faith attempts to sort out misunderstandings, where the parties involved turn out to have very different interpretations of the same signal. For example, the phrase “quite good” can be interpreted as damning with faint praise (the bottom left quadrant of the plot) or as flattering understatement (the top left quadrant of the plot).

This ties in with concepts such as shock and humour, where the nature of a misunderstanding can be modeled in terms of Necker shifts; the greater the distance between the two possible intepretations, the more horrifying or funny the outcome is.

This representation is also useful for teaching communication. For example, it can be used in assertiveness training to help people learn phrasings that will let them move a conversation more efficiently in the direction that they want (e.g. sending out a signal that is positive, but not too positive). It can also be used to teach patterns of interaction, such as how to de-escalate a situation.

This approach can also be extended to model multiple layers of communication; for example, showing what each participant thinks that the other participant really means, in conversations where neither party believes that the other is acting in good faith.

So, in summary, this visualisation is simple, but can give powerful insights into communication.

Notes, references and links

You’re welcome to use Hyde & Rugg copyleft images for any non-commercial purpose, including lectures, provided that you state that they’re copyleft Hyde & Rugg.

There’s more about the theory behind this article in my latest book: Blind Spot, by Gordon Rugg with Joseph D’Agnese 

You might also find our website useful:

1 thought on “Modeling misunderstandings

  1. Pingback: Games people play, and their implications | hyde and rugg

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