RM: It wasn’t “damage control”. It was simply pointing out an essential fact about what Powers was referring to as the “organism function” in the article we have been discussing. You were right that qo = f(qi) is the “organism function” in a control diagram. But because Powers paper was about how scientific psychologists go about trying to determine the organism function, he wrote the organism function as qo = f[h(qd)].
Sorry, I thought it was damage control.
To me, it seems like “the organism function” is always F, defined in equation (1) qo = F(qi). Bill is very consistent about it in the paper. The equation qo = f(h(qd)) is not the organism function, and he doesn’t refer to it as the organism function. It is the solution for a zero-feedback system for qo, meaning “how will qo depend on other variables in the system”.
In the text you highlighted, he is saying that the organism function F is replaced by the feedback function G’s inverse in the solutions. He is comparing to equations, solution for qo for an N system, and solution for qo for a Z system. He is also saying that qi* can be taken as zero. Let’s also put a name to H(qd), to simplify the expressions:
(1) qi* = 0
(2) qe = H(qd)
(3) qo = G^-1 [ qi* - H(qd) ]
(4) qo = G^-1 [ H (qd) ]
(5) qo = G^-1 ( qe )
Equation (3) is a solution for qo for a negative feedback system taken from the paper, and equation (5) is a slightly simplified form.
(6) qo = F [ H (qd) ], using (2):
(7) qo = F ( qe )
Equation (6) is a solution for qo for a zero feedback system taken from the paper, and equation (7) is a slightly simplified form.
Specifically in the sentence where you highlighted “organism function”, he is referring to these two equations:
N-system equation: (5) qo = G^-1 ( qe )
Z-system equation: (7) qo = F ( qe )
In the N-system equation, qo is determined by the feedback function’s inverse of qe. In the Z-system equation, the qo is determined by the F function of qe. That is why he says “the organism function F in the z-system equation is replaced by the feedback function g^-1 in the N system equation”.
RM: So while conventional psychologists are actually looking at the relationship qo = f[h(qd)] they assume they are looking directly at the system function qo = f(qi).
If they are looking at an N system, they are looking at qo = G^-1 ( H (qd) ], or simplified (5) qo = G^-1(qe), but they assume they are looking at (7) qo = F (qe). They have misidentified an N system, thinking it is a Z system.
If they measure this in an experiment:
qo = 0.2 * qe
They will think that F(x) = 0.2 * x. That is the behavioral illusion, because F might really be F(x)= integral (1000x) or whatever, and the 0.2 was determined by their experimental setup where they had some G function G(x) = 5 * x.
RM: I meant that when the topic of discussion is the behavioral illusion as described in Powers (1978) – an illusion that results from failure to take into account the fact that qd and qo have opposing effects on a controlled variable , Qi, whatever that variable may be – it seems like the discussion should always focus on the fact that the illusion occurs because the existence of controlled variables is being ignored or missed.
I think that ignoring the existence of controlled variables is a consequence of having a wrong model of organism behavior. There is no such thing as a controlled variable if the model of behavior is a lineal causation, stimulus-response, R = O(S), which is equivalent to (7) qo = F(qe).
The behavioral illusion happens because of adopting (7) as the model of organism behavior and trying to find the organism function O by relating stimuli to responses. Sure, they are also ignoring controlled variables and dynamics of feedback systems and so on, but I think the core of the illusion is the R = O(S) model. An error in system identification.
RM: I never thought the power law was an example of the behavioral illusion described in Powers (1978).
M&S (2018): In the present paper we answer these claims and show that the power law of movement is, indeed, an example of a behavioral illusion.
[…] we showed that this assumption is likely to be based on what Powers (1978) called a behavioral illusion
The title of the paper - “Power law as behavioral illusion” - really sounds like you think (or thought at the moment of writing) that the power law is an example of the behavioral illusion, as defined in 1978 paper. Now it sounds like you’ve changed your mind.
As for the side effects of control not revealing something about the organism, we might disagree there too, as side-effects often do reveal “something” about the organism (reaction time reveals something about the level of control, maybe), but that is a whole different discussion not related to the behavioral illusion.
RM: So let’s just leave it at our agreeing that the power law is not an example of the behavioral illusion described in Powers (1978).
Great, fine with me.