[From Kent McClelland (2012.09.26.2005)]
The discussion of conflict, low gain, and dead zones in the "PCT Lament and Conflict" thread has been fascinating and informative from my point of view, and even though I haven't found the time to contribute to it myself, the exchange has made me glad that I've started following CSGnet again, after a substantial time away. It's really nice to see the current traffic on this forum zeroing in on questions directly related to the development of PCT, rather than chasing off all the time after side issues. Thank you, Martin, Rick, and Bill.
As I've worked my way through these posts, some of which have been pretty technical and not all of which I'm confident I understand, a number of questions have occurred to me, mostly connected with the idea of loop gain, which seems central to a lot of issues that interest me. Let me put them in the context of some recent posts:
[Bill Powers (in an undated post that I received on 2012.09.20.1030)]
BP: This [escalating conflict between two systems] actually depends on the loop gain of the combined control systems. This can be determined by tracing total gain around the two-system loop from any variable back to itself. Starting with one CV, we have the gain of the input, comparison, and output functions, follow by the gain of the connection from one system's output quantity to the CV of the other system, then through the other system in a similar way and back to the CV of the first system. At the same time, the feedback function of each system subtracts some amount from the magnitude of its own CV. If the input-to-output gain is high in both systems, it won't take much effect of the action on one system on the other CV to reach a threshold where the composite loop gain minus the local feedback function's gain exceeds unity, the threshold of static instability.
KM: Where can I look for some technical guidance on how to compute "composite loop gain"? I'd like to try calculating it for some of my simulations of conflict. And is the "threshold of static instability" the same thing as the "critical" value for total gain of two conflicting systems that I talked about in one of my earlier posts (Kent McClelland 2012.09.19.1029 MDT)?
In the discussion of dead zones vs. lowered gain that has been the centerpiece of the "PCT Lament and Conflict" thread, I wonder if it would help in thinking about these issues to make a sharper distinction between input gain and output gain, as Bill Powers (2012.09.28.0945) and Rick Marken (2012.09.28.1100) have started to do in their most recent posts. Is the dead zone that you've been talking about a dead zone on the input function or the output function? I could see it possibly working either way.
In the input function we might be understanding a dead zone as a threshold effect, where low levels of a particular input are not even registered as a perception (as when we need a certain level of brightness even to see a star at night), but above that threshold differences in the intensity of the input begin to be registered on a continuous scale of some kind. Or there might be some strong nonlinearities in the input function at the extremes of the scale being perceived, which would make it look like there is a dead zone at the bottom. And could low input gain make it seem like there is a dead zone, because perceptions with low gain are just not as sharp as high-gain inputs and thus might miss phenomena that to be perceived at the extremes of a scale? (Though this last seems pretty remote, I mention the possibility because stable equilibrium control with a low-gain control system leaves a bigger gap between the perception and the reference than with a high-gain control system.)
In the output function we might talk about a dead zone as a region of no output that happens because the control system is in passive-observation mode, as Bill describes it in B:CP. (Have I got the terminology right? I don't have a copy of B:CP with me at the moment to check it out.) And then a higher-level control system starts sending reference signals to the lower-level system in passive mode because the deviation from some standard at the lower level has reached a point that threatens the stability of a perception and requires adjustment at the higher level. A possible scenario: you hear a motor noise and pay no attention--don't even notice it, although it's registering out of consciousness--but then it begins to get louder and some higher-level control system begins to interpret it as an approaching vehicle, and you jump aside to save your skin.
So, would a dead zone be in input or output, both or neither?
Finally, I'm really interested in people's thoughts on perceptions with gains high enough that they approach or pass the "threshold of static instability", as Bill describes it in the post I quoted above. It seems to me that perceptions like that are interesting for a variety of reasons.
For one thing, I see the learning process as a progression in raising that threshold for a given perception. As we become more practiced and skillful in a given perception, we can control it at a higher level of gain without having it blow up in our faces, as it were.
Second, and related, it seems to me that activities that we describe as play, particularly children's play, but also many recreational pursuits for adults, involve explorations of those limits of control, seeing how much one can jack up the gain before the process goes unstable, seeing if one can operate on the knife-edge of instability. The dangerous pursuits, like rock climbing, that are also exhilarating and fun must be like that. And the sense of "flow" that comes from these activities must have to do with the concentration needed for maximal performance (like devoting all of the gain resources at one's disposal to the activity and and turning down the gain on everything else). As a sociologist, I'm particularly interested in collective activities that might operate on this level of maximal stable gain. I have a lot more I might say along this line, but I'll stop here and see if anyone thinks I'm barking up the wrong tree.