multidimensional conflict

[Martin Taylor 2013.04.30.23.53 PDT]

>From Kent McClelland (2013.04.29.1130 CDT)]

[KM] As it happens, I played around years ago with models of two-dimensional conflicts, in which the perceptions controlled by two agents are linear functions in an X-Y plane. Each agent is modeled as having two outputs, one working in the X direction, and the other in the Y.

Just as Rick suggests, I tried to see what happens when you vary the correlation between the two lines that represent the references for the two simulated agents. At the time, I wasn't sure how to relate this modeling work to empirical situations, but your comments have suggested to me some ways these models could be applied. Here's what I found:

Situation A: When the two preference lines are parallel to each other (do not intersect), you get conflict dynamics similar to the one-dimensional situation, with unlimited escalation of output in opposite directions (perpendicular to the preference lines).

B: When the two preference lines are orthogonal to each other, and the initial position of the environmental variable is at a point different from the intersection of the two lines, the combined outputs of the two agents quickly bring the environmental variable to the point of intersection of the lines of preference, and then the agents hold it at that compromise point (approximately) against any random disturbances in the X-Y plane.

C: When the two preference lines meet at an acute angle and thus are somewhat correlated, the outputs of the two agents bring the environmental variable quickly to some point along a center line that splits the difference between the two preference lines, but not immediately to the point of intersection of the preference lines. Then, more slowly, their combined outputs pull the environmental variable along that compromise line till it gradually reaches the point of intersection of the two preference lines. When the environmental variable has finally reached this compromise point, the two systems hold it approximately there against disturbances.

Kent,

What you describe is not 2-D conflict, but illustrates what I would call interference between control of two perceptions that ranges from zero (actions that influence one perception do not influence the other) to complete conflict (the two perceptions cannot both arrive at their reference levels at the same time). Interference makes control of at least one of the perceptions more difficult, and complete interference makes control of at least one impossible.

Conflict, true conflict rather than strong mutual interference, occurs when there are more degrees of freedom in the perceptions to be controlled than there are in the means to control them. The 1-D conflict is just a special case.

Imagine, for example, using the X-Y position of a mouse to control perceptions of a grey disc, the perceptions to be controlled being the shade of grey, the diameter of the disc, and the left-right location of the disc in its window. It can't be done. You can control any two, but not the third at the same time. If you add another perception, such as the vertical position of the disc in its window, you can still control any two, but disturbances in the other two must go unopposed. The conflict isn't in any one pair of controlled perceptions that correspond to the same environmental variable. It's intrinsic to the set of them.

In the "standard" conflict, the limiting degrees of freedom are in the environment. In the example above, the limit is in the means of influencing the environment. The effect is the same. Let's modify the example to put the limit into the environment. Assume you have two mice, so you could influence all four of the environmental variables. But now something in the environment links the disc's shade, diameter, and position so that if you think of each as being represented by a number between zero and 100, the four of them always sum to 200. If you control any three to their reference values, you suddenly find that you can't adjust the fourth without altering at least one of the others. The set of four values has only four degrees of freedom, and one of those has been fixed by setting the overall sum, which leaves only three for control, even though you have four degrees of freedom for mouse movement.

Put this into a more general context of competition for limited resources (the limit being analogous to the sum in the previous paragraph), and the conflict becomes manifest in the rich taking resources that are then unavailable to the poor -- in a conflict, the system with the stronger output can overwhelm the weaker system, whether the conflict is 1-D or exists within a high-dimensional set of interactions. In the resource case, money provides power, but so does physical force, and if the conflict is resolved completely one way by the power of money, it might later be resolved in the other by revolution.

I think multidimensional conflict is rather more interesting than one-dimensional, though I do not know whether it involves novel insights or structures beyond what can be seen in a 1-D conflict.

Martin

Hi Martin,

Thanks for your comments. I think I see exactly what you're saying, but since it adds some complications to my previous ways of thinking about these matters, I'll need to mull it over for a while before making a reply. Thanks again.

Kent

···

On Apr 30, 2013, at 10:58 PM, Martin Taylor wrote:

[Martin Taylor 2013.04.30.23.53 PDT]

>From Kent McClelland (2013.04.29.1130 CDT)]

[KM] As it happens, I played around years ago with models of two-dimensional conflicts, in which the perceptions controlled by two agents are linear functions in an X-Y plane. Each agent is modeled as having two outputs, one working in the X direction, and the other in the Y.

Just as Rick suggests, I tried to see what happens when you vary the correlation between the two lines that represent the references for the two simulated agents. At the time, I wasn't sure how to relate this modeling work to empirical situations, but your comments have suggested to me some ways these models could be applied. Here's what I found:

Situation A: When the two preference lines are parallel to each other (do not intersect), you get conflict dynamics similar to the one-dimensional situation, with unlimited escalation of output in opposite directions (perpendicular to the preference lines).

B: When the two preference lines are orthogonal to each other, and the initial position of the environmental variable is at a point different from the intersection of the two lines, the combined outputs of the two agents quickly bring the environmental variable to the point of intersection of the lines of preference, and then the agents hold it at that compromise point (approximately) against any random disturbances in the X-Y plane.

C: When the two preference lines meet at an acute angle and thus are somewhat correlated, the outputs of the two agents bring the environmental variable quickly to some point along a center line that splits the difference between the two preference lines, but not immediately to the point of intersection of the preference lines. Then, more slowly, their combined outputs pull the environmental variable along that compromise line till it gradually reaches the point of intersection of the two preference lines. When the environmental variable has finally reached this compromise point, the two systems hold it approximately there against disturbances.

Kent,

What you describe is not 2-D conflict, but illustrates what I would call interference between control of two perceptions that ranges from zero (actions that influence one perception do not influence the other) to complete conflict (the two perceptions cannot both arrive at their reference levels at the same time). Interference makes control of at least one of the perceptions more difficult, and complete interference makes control of at least one impossible.

Conflict, true conflict rather than strong mutual interference, occurs when there are more degrees of freedom in the perceptions to be controlled than there are in the means to control them. The 1-D conflict is just a special case.

Imagine, for example, using the X-Y position of a mouse to control perceptions of a grey disc, the perceptions to be controlled being the shade of grey, the diameter of the disc, and the left-right location of the disc in its window. It can't be done. You can control any two, but not the third at the same time. If you add another perception, such as the vertical position of the disc in its window, you can still control any two, but disturbances in the other two must go unopposed. The conflict isn't in any one pair of controlled perceptions that correspond to the same environmental variable. It's intrinsic to the set of them.

In the "standard" conflict, the limiting degrees of freedom are in the environment. In the example above, the limit is in the means of influencing the environment. The effect is the same. Let's modify the example to put the limit into the environment. Assume you have two mice, so you could influence all four of the environmental variables. But now something in the environment links the disc's shade, diameter, and position so that if you think of each as being represented by a number between zero and 100, the four of them always sum to 200. If you control any three to their reference values, you suddenly find that you can't adjust the fourth without altering at least one of the others. The set of four values has only four degrees of freedom, and one of those has been fixed by setting the overall sum, which leaves only three for control, even though you have four degrees of freedom for mouse movement.

Put this into a more general context of competition for limited resources (the limit being analogous to the sum in the previous paragraph), and the conflict becomes manifest in the rich taking resources that are then unavailable to the poor -- in a conflict, the system with the stronger output can overwhelm the weaker system, whether the conflict is 1-D or exists within a high-dimensional set of interactions. In the resource case, money provides power, but so does physical force, and if the conflict is resolved completely one way by the power of money, it might later be resolved in the other by revolution.

I think multidimensional conflict is rather more interesting than one-dimensional, though I do not know whether it involves novel insights or structures beyond what can be seen in a 1-D conflict.

Martin

[From Bill Powers (2013.05.05.1655 MDT)]

Hi Martin,

Thanks for your comments. I think I see exactly what you're saying, but since it adds some complications to my previous ways of thinking about these matters, I'll need to mull it over for a while before making a reply. Thanks again.

...

>> [KM] As it happens, I played around years ago with models of two-dimensional conflicts, in which the perceptions controlled by two agents are linear functions in an X-Y plane. Each agent is modeled as having two outputs, one working in the X direction, and the other in the Y.

BP: Take a look at Demo 7-2, ThreeSys, in LCSIII. In this demo, the perceptual input functions of three control system each sense the weighted sums of three environmental variables, the weights being set at random. After new input weights are set, the output weights reorganize the weights through which each one affects all three EVs. (I have versions of this demo that go as high as 500 systems in operation simultaneosly but slowly, sensing and affecting 500 environmental variables). In Demo 7-2, you can click a button and get a new set of weights at any time. The systems then reorganize their output function connection weights to the EVs to minimize overall squared error. The idea was to see if the output weights would reorganize to equal the transpose of the input weights. In Demo 6-1, Live Three, setting output weights that way always seems to result in stable unconflicted control, and Richard Kennaway, I think, verified that. Amazing. I don't know if 7-2 really verifies that but it also always results in stable control.

There is a button in 7-2 that generates a new set of random weights, and this process keeps testing new sets very rapidly until one is found that creates a specific range of values of the determinant of the input matrix. A slider selectes the desired range. In effect, the slider selects the degree of orthogonality of the new input matrix. A determinant of zero means there is no solution for the simultaneous equations (maximum conflict), and a determinant of 1 means that the three systems detect completely orthogonal perceptual signals -- any perceptual signal can then be altered without disturbing either of the others (no conflict, or very little since there is a small range of determinant values).

The simplest indicator of degree of conflict is in the behavior of the environmental variables being affected by the three system outputs. The lower the input orthogonality, the more likely it is that one output will disturb the perceptions in the other two control systems, so the final control systems cause large amounts of output while making the three perceptual signals match the three changing reference signals. Even with determinants close to 1.0, control is always achieved (with occasonal bursts of instability), but the cost in terms of output effort gets very large.

This suggests use of a quantitative scale of conflict rather than a categorical measure (conflict or no conflict). Where you draw a line and say any greater degree of effort indicates conflict is somewhat subjective. However, as Kent discovered, if the output functions have limits of output that they can produce, serious effects of conflict appear when one more more output functions reaches its limit. Control becomes impossible for at least one of the systems and errors rapidly escalate.

When larger numbers of systems are involved, the potential for conflict increases. I haven't done much with exploring that range of parameters.

Best,

Bill P.

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At 04:27 PM 5/1/2013 +0000, McClelland, Kent wrote:

[From Rick Marken (2013.05.06.0900)]

Bill Powers (2013.05.05.1655 MDT)

BP: The simplest indicator of degree of conflict is in the behavior of the environmental variables being affected by the three system outputs. The lower the input orthogonality, the more likely it is that one output will disturb the perceptions in the other two control systems, so the final control systems cause large amounts of output while making the three perceptual signals match the three changing reference signals. Even with determinants close to 1.0, control is always achieved (with occasonal bursts of instability), but the cost in terms of output effort gets very large.

RM: I understand this in terms of linear algebra. What I don’t have a good handle on is what this means in terms of real life experience (which is what most people really want to understand using PCT). So what would really help us get a better grasp of the “perceptual basis” of conflict is if you could give a few “real life” examples of orthogonal (or slightly orthogonal) perceptions of the same environmental variables which, when controlled by two different control systems (people), result in no conflict. I can understand it in terms of pairs of lines of lengths x and y on a computer screen, where it’s possible for one person to control x+y while the other controls x-y sans conflict. But I think a more flesh and blood example would be a lot more interesting to those who are interested in PCT as a basis for understanding human (and societal) psychopathology.

Best regards

Rick

···


Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com