AM: 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.
RM: The function qo = f[h(qd)] is the organism function from the point of view of scientific psychologists who view organisms as Z-systems. This equation is equivalent to the organism function in equation (1) because qi = h(qd) and experimental psychologists assume that h() is a multiplier of 1. And Bill certainly does refer to the f function in the equation for a Z-system – qo = f[h(qd)] – as “the organism function” when he says " …the organism function f in the Z-system equation is replaced by the inverse of the feedback function g-1 in the N-system equation".
AM: 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 )
AM: 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: That’s mathematically correct because you have defined qe = h(qd). This hides the fact that it is qd – not qe – that is manipulated in a psychology experiment. Thus, you have effectively “buried the lede” of Bill’s paper, which is as follows: The foundation of experimental psychology is that DV = f(IV) or, in Bill’s terms, qo = f(qd), where f() represents functional characteristics of the organism under study.This foundational assumption is wrong if organisms are N-Systems.
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).
AM: 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.
RM: Conventional psychologists can’t be looking at qo = G^-1(qe) or qo = F(qe) because they can’t see qe! The whole point of the 1978 paper is that experimental psychologists have been studying relationships between qd’s and qo’s (IV’s and DV’s) thinking that those relationships, when they are found, tell them something about the nature of the organism’s under study; about the organism function, f. But, in fact, they are looking at the inverse of the feedback function that relates qo to qi.
RM: By writing your equations in terms of qe, you have managed to conceal (from your readers as well as from yourself) the main point of Powers’ 1978 paper, which is: You can’t tell anything about the behavior of a living control system – an N-System – by studying relationships between independent (stimulus) and dependent (response) variables. In order to understand the behavior of a living control system you have to determine what variables it is controlling. This is the truly revolutionary point of PCT.
AM: If they measure this in an experiment:
qo = 0.2 * qe
RM: They can’t (and don’t) measure that in an experiment because they can’t measure qe. If they could, they would be measuring qi and they would, thus, already be doing PCT based experiments. But what conventional experimental psychologists can (and do) measure in an experiment is qd, the disturbance (IV) and qo, system output (DV).
AM: 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: The behavioral illusion doesn’t result from an error in system identification; it reveals an error in system identification. And it shows that this error in system identification results from failure to see that the system is a control system – an N- System – controlling perceptual aspects of its own environment. Once you know that you have made this error you can stop studying the system as though it were a cause - effect system – a Z- System - and start studying it knowing that is is an N - System. And that means you can start doing research aimed at identifying the variables the system controls rather than the variables that “control” (or cause the behavior of) the system. Because there are no such variables.
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
RM: In English (and, according to linguist John McWhorter, in all European languages) articles are very important. So notice that I referred to “a behavioral illusion” (using the indefinite article “a”) rather than “the behavioral illusion” (using the definite article “the”). Once you understand that organisms are N- rather than Z- Systems you can see that experimental psychologists have been subject to several illusions, all of which result from failure to notice controlled variables. Another obvious illusion – one that Powers has discussed (though not in the 1978 paper) – Is the reinforcement illusion; the illusion that consequences select actions when, in fact, actions control consequences.
AM: 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.
RM: That time I left out the article. In English that implies the indefinite article. I did that on purpose because I was well aware of the fact that the power law is not an example of the S-R illusion that Powers describes in the 1978 paper. In both of our papers on the power law I tried to make clear what we meant by “behavioral illusion”. Here’s a quote from the second paper: " …a behavioral illusion occurs when an observed relationship between variables is seen as revealing something about the mechanisms that produce a behavior when, in fact, it does not". The power law (like the S-R illusion) is a behavioral illusion in this sense.
AM: 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: Reaction time is not a side effect of control; it is as aspect of control system operation.
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).
AM Great, fine with me.
RM: But I do admit that I am interested in knowing what you think the power law tells us about how an N-System produces curved movements. Well, maybe not that interested;-)