[Martin Taylor 2012.09.23.10.13]
[From Bill Powers (2012.09.23.0650 MDT)]
Rick Marken (2012.09.22.1820)
> Martin Taylor (2012.09.22.18.51)--
> RM: I think Martin's acceptance zone model is unlikely to be the way things
> work -- with a zone of acceptance around zero error.
>
> MT: Why not?RM: Because I have never seen any data that suggests that it's necessary.
OK, let's talk about driving a car, always a source of good examples. Here you are in your lane with a gusty crosswind blowing, and you see the car is centered in its lane, so you don't need to turn the steering wheel. Now a little gust comes by and the car suddenly moves left of its reference position by one millimeter. By how much do you turn the steering wheel to the right?
I was intending a response in the same vein, but you have said enough to make the point.
I think it would not be too hard to included a dead-zone adjustment and see if it improves the fit of the model to the data, and how big the dead zone is.
I'm going from distant memory here, but my memory says that with a positional pursuit tracking task with stepwise disturbance waveform, where the relative location of the target and the cursor was easy to see, my dead zone was about 0.6 pixels. If it is harder to see whether the target is above or below the cursor, the zone will probably be wider.
Your examples, including the one I quoted, argue that in everyday situations the width of the dead zone is controllable. If the driver is vying for a million-dollar prize given to the driver keeping closest to the lane centre, the millimetre deviation (presumably detected with some kind of a technological device) might well be corrected, whereas on the same road it would not be when the driver was just going to visit Aunt Millie. At a less contrived level, how much deviation from lane centre do you tolerate on an empty country road with good visibility for other traffic as compared to driving the same road when the traffic is heavy?
Personally, I don't think that the dead zone ever has a well defined boundary. The dead zone in my graph does, but I drew that to make a point about conflict. I don't have any evidence, but it seems more probable to me that a more realistic graph would show a slope increasing from zero at the origin to some finite value (such as 1.0, if we assign the gain to the output function).
More generally, if you want to find dead zones that are not simply a way of getting around noise in the comparator's input signals, you have to set up a conflict situation. For example, try two simultaneous pursuit tracking tasks using one mouse movement and a switching action (such as a click) to transfer the effect of mouse movement from one task to the other. You will be unable to track either precisely, but if the disturbance bandwidth is not too high, you will be able to track both within a tolerable error bound. In the everyday world, when you say "that's good enough", such as when you finish an e-mail message and decide to send it, it is often because you want to do something else.
Martin