From: Richard Marken [mailto:email@example.com]
Sent: Thursday, October 12, 2017 1:09 AM
Subject: Re: Behavioural Illusion (was Re: What is revolutionary about PCT?)
[From Rick Marken (2017.10.11.1608)]
Bruce Abbott (2017.10.09.2240 EDT)
Rick Marken (2017.10.09.1030) –
RM: The relationship between disturbance and output is not causal. The causal link from disturbance to output is “erased” by the simultaneous effect of the output on the controlled variable.
HB : Which is what ?
RM : The actual cause of the output in a closed loop is the controlled variable itself.
HB : Do I understand right that perceptual variable (the controlled variable) is the actual cause of output ?
RM : But this causal connection is difficult to see – especially when control is good --because the effect of the CV on output is quickly reduced by the output itself.
HB : Can you translate this into PCT language ?
BA: Letâ€™s trace the events once around the loop. (I assume a constant reference value.) The disturbance causes the controlled variable (CV) to change, which causes the sensed input to change, ……
HB : Sorry Bruce I donâ€™t understand quite. Does this mean that there is â€œcontrolled variableâ€? in environment of control system that is changed by disturbances and then they â€œbothâ€? change perceptual signal, the controlled variable.
Bill P : FEED-BACK FUNCTION : The box represents the set of physical laws, properties, arrangements, linkages, by which the action of this system feeds-back to affect its own input, the controlled variable. That’s what feed-back means : it’s an effect of a system’s output on it’s own input.
HB : Is this what you meant ?
BA : ….which causes the perceptual signal to change, which causees the error signal to change,
HB : You probably meant that perceptual signal with references â€œmismatchâ€? the result (error-signal)
Bill P (B:CP) : ERROR : The discrepancy between a perceptual signal and a reference signal, which drives a control systemâ€™s output function. The discrepancy between a controlled quantity and itâ€™s present reference level, which causes observable behavior.
Bill P (B:CP) : ERROR SIGNAL : A signal indicating the magnitude and direction of error.
Bill P (B:CP) :
COMPARATOR : The portion of control system that computes the magnitude and direction of mismatch between perceptual and reference signal.
BA : …which causes the output to change which causes the ffeedback output to change in a direction opposite to that of the disturbance. All this takes place in the time it takes these causes to propagate around the loop. At no point is the series of causal links between disturbance and output broken.
HB : We already talked about the Â»comparatorÂ« which breaks the casual loop. Abstractly in Bills’ diagram it maybe looks like that everything is smooth and matematically perferct, but in real organism that is not so.
RM: The problem is in the step where the disturbance causes the CV to change.
HB : For you that was always a problem. You are looking for the problem on wrong place.
RM : It’s actually the simultaneous effect of the disturbance and output that causes the CV to change.
HB : Which Â»CVÂ« ?
RM : That makes all the difference. And it’s why you will not find a causal path through the organism from disturbance to output.
HB : This is not the reason why you’ll not find the casual pathaway from input functon to output. The reason is how nervous system function. Â»ComparatorÂ« is not acting like a simple Â»casualÂ« function. Â
BA: The feedback from previous circuits around the loop does not erase the effect of the disturbance, even if on this particular trip around the loop the feedback happens to equal the effect of the disturbance on the CV. To see that this is so, I present the simple case in which the error and output are currently zero and a disturbance is suddenly applied to the CV and held constant. This disturbance causes the input to change, which causes the perceptual signal to change, which causes the error signal to change to some nonzero value. This error is multiplied by the output gain. In our digital simulations, if the resulting high output were to be applied full force to the feedback function, the huge level of feedback would drive the system into destructive oscillation. This is because time is being left out of the calculations, as if the output could be applied instantaneously at full force. But real systems change over some finite period of time. To bring time into the computations, we impose a â€œleaky bucketâ€? integration to the output, which causes the output to rise as a negative exponential function over iterations. Only a small portion of the total change in output that would otherwise be produced by the error signal is allowed to appear, and this then determines the level of feedback that is applied to the CV on this cycle around the loop.
BA: On the next cycle around the loop, the effect of the disturbance on the CV is now being opposed by a only small fraction of what the feedback would otherwise have been. The same level of disturbance is present, but its effect on the CV is now being partly compensated for by the feedback. The smaller net effect on the CV causes a smaller change in input value from its initial value, which causes a smaller change in perceptual signal, which causes a smaller error signal. Due to the leaky integrator nature of the output function, the output rises by a small portion of the difference between its present and final levels until feedback and disturbance effects on the CV are equal and opposite. It takes a few trips around the loop for the full effect of the disturbance on the feedback level to appear, nevertheless, it is the disturbance that is the ultimate cause of the change in feedback.
BA: Only a portion of the change in output that would be necessary to fully compensate for the disturbance can occur on each iteration, but this merely spreads the cause-effect chain across several iterations of the loop. It in no way â€œerasesâ€? that effect. The effect of the disturbance is taken apart, transmitted in small packets across several iterations, where their effects are in effect reassembled by the output function to produce the full level of compensatory feedback.
BA: By the way, analog systems do not normally require a leaky integrator as changes in physical variables naturally require time to complete.
Richard S. Marken
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.â€?
–Antoine de Saint-Exupery