AM: The feedback function is relating qo to an effect on qi, what Bill in programs for the analog computer and Bill and Bruce Abbott in LCSIII called the feedback quantity. The name is appropriate, I think, because it is another environment quantity, along with input, output and disturbance quantities, in contrast to perceptual, reference and error signals. I’m not saying that is the only correct name, I just think it is nicely chosen. ‘Feedback effect’ is also good.
RM: I agree that it’s important to keep in mind that the feedback function, g(), converts system output, qo, into an effect on the controlled variable, qi. But it’s also important to keep in mind that the same is true of the disturbance; the disturbance function, h(), converts the disturbance quantity, qd, into an effect on the controlled variable. This is shown in Figure 1 from the the 1978 paper:
RM: The effects of output and disturbance on the controlled variable are represented as g(qo) and h(qd) in this diagram. If you added the variable qf to this diagram to explicitly show the feedback effect on qi I think you should also add a variable such as qe to the diagram to explicitly show the effect of the disturbance on qi: qe = h(qd). This might make things clearer from your perspective but i think it’s unnecessary.
AM: You also wrote in the previous post (twice) that the organism function is relating qd and qo, that is not correct. The organism function is relating qi and qo.
RM: Actually, we are both correct. The organism function is qo = f(qi), per equation 1 in Powers (1978). However Powers’ paper is a critique of scientific psychology in general and the experimental method used in the field in particular. In conventional scientific psychology the experimentally determined relationship between qd (IV) and qo (DV) Is thought to tell us about the nature of the organism. This is done under the assumption that the system under study is either a Z- system (no feedback effect of qo on qi) or, if an N-System, a system where the feedback makes little difference.
RM: So in Powers analysis the organism function assumed by scientific psychologists is taken to be qo = f[h(qd)] (last equation on p. 423). This is derived from the organism function above and the environment function qi = g(qo) + h(qd) (equation 2 in Powers (1978)) under the assumption that g(qo) - the feedback effect of output – either doesn’t exist (Z -system) or doesn’t matter.
RM: The assumption in scientific psychology is that the function h() is essentially a multiplier of one. So in the conventional psychology experiment, when qd is manipulated and concomitant variation in qo is observed, the researcher assumes that what is being seen is an approximation to the organism function, f(), since qo = f(qd) (or DV = f(IV)). Powers (1978) shows that what is actually being seen is an approximation to qo = g-1(-qd).
AM: Some notes: in the simulation, the F function is an integrator, it accumulates values, meaning that its output value depends not only on the input, but also on previous values of output. This could be further explored, to see the relationship between qi and the derivative of qo, it gives nice plots, too, in some simulations. But, that is also the reason why qi-qo is not a nice linear plot.
RM: All this assumes that qi is a simple scalar variable. In most tracking tasks this is probably close to being the case. But the kinds of variables controlled by living organisms – particularly people – can be pretty complex functions of simpler perceptual or environmental variables. So whatever relationships between qi and qo you find to hold for scalar qi may not hold for more complex qi’s. Why not try modeling control of some of the qi in STEP H: BEYOND TRACKING of your beautiful reproductions of Bill’s demos at http://www.pct-labs.com/tutorial1/index.html. See if the type of variable controlled makes a difference in your conclusions about the relationships between variables in a control loop.
AM: Another direction for exploring starts from the fact that the inverse of integrating is derivating. Putting an integrator in the feedback path can make the qd vary as a derivative of qo.
RM: THe feedback path shouldn’t affect the disturbance. I think what you mean is that it would make qo vary as the derivative of qd, which should be true.
AM: This is a discussion strictly about the behavioral illusion, as the title says, not about all the other possible blunders or artifacts or general consequences of mistaking N systems for Z systems, etc, etc, so I’m sticking to the topic of the behavioral illusion and not discussing controlled variables or other things.
RM: I don’t see how you can make any sense of the behavioral illusion discussed in Powers (1978) without discussing controlled variables. The illusion turns on the fact that the existence of a controlled variable is being ignored or simply missed. It seems to me that discussing the behavioral illusion without discussing controlled variables is like discussing the bent stick illusion without discussing the differential refraction of light in air and water.
RM: And I also wonder why you are fixated on the S-R behavioral illusion described in Powers (1978). It doesn’t seem relevant to your power law of movement research. It’s only relevant to research where an environmental variable (qd) is manipulated under controlled conditions to determine whether there is concomitant variation in a behavioral variable (qo). In the power law research both variables involved in the power law – curvature and speed of movement – are behavioral variables. So there is no controlled variable being disturbed by one of those variables and protected from that disturbance by the other.
RM: First of all, if the system under study is an N-system then you have to know what variables the system is controlling in order to know whether any observed relationship between environmental and behavioral variables is one between qd and qo. That’s because qd is defined as a disturbance to a controlled variable, qi, and qo is defined as a behavioral output that compensates for the effect of that disturbance to qi. So you can’t do your proposed demonstration until after you have done some form of the test for the controlled variable.
AM: Yes, I perfectly agree with that, especially the bold part.