Minding your p's and Qi's: Adaptation

[From Bruce Abbott (2017.02.24.1220 EST)]

In a well-known demonstration, there are three buckets of water, one cold, one hot, and one half-way between those two temperatures. You place your left hand in the cold water and your right hand in the hot water and let them soak for a short while. Then you place both hands into the same medium-temperature bucket. What you experience is that the water in this bucket feels hot to your left hand and cold to your right hand – for a short while at least. It’s a bizarre experience: you know that both hands are immersed the same water, yet you perceive the temperature of the water as different.

What you are experiencing is due mainly to the fact that sensors for skin temperature respond much more strongly to changes in skin temperature than they do to a constant skin temperature. After your hands have soaked for a time in the initial buckets, their skin temperature has come to equilibrium with the temperature of the surrounding water: the left hand is cold and the right hand is hot. When you then place both hands in water of an intermediate temperature, the skin of your left hand rapidly warms, generating a perception of strong warmth, while the skin of your right hand rapidly cools, generating a perception of strong cold. As the skin temperature of both hands approaches equilibrium with the surrounding water, the difference between these two perceptions diminishes and eventually vanishes.

I bring up this example to illustrate how the relationship between an environmental variable Qi and its perception p may change as a consequence of exposure to conditions. Now imagine that you are trying to control the temperature of your bathwater by dipping your hand into the water while the tub is filling and then adjusting the temperature of the water coming out of the spigot. In the end the water in the tub feels about right and you get into the tub. Initially the water feels satisfyingly hot to you, but after a short while it seems to have cooled considerably and you begin to add more hot water to bring the temperature up. Some of the apparent cooling may be real – the water is gradually losing heat to the environment, after all. However, most of the apparent cooling may actually reflect the fact that your skin temperature has come to equilibrium with the temperature of the water, and this has caused a reduction in output from the temperature sensors in your skin. You still have the same reference for the temperature you perceive, but you now perceive the temperature to have fallen a good deal (p is much lower) when in fact the water temperature has hardly changed (Qi is nearly constant). You add hot water to bring that perception back to reference, and consequently the bath is now much hotter than it was initially – although it now feels like it is merely back to your preferred temperature, r. You continue to control p to your reference value, but to the external observer it looks like you have increased your reference level for Qi.

Cases like this demonstrate why it is important to understand that control systems control p directly, and control Qi only indirectly through the linkage between Qi and p.

Bruce

[From Rick Marken (2017.02.24.2100 PST)]

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Bruce Abbott (2017.02.24.1220 EST)–

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BA: In a well-known demonstration, there are three buckets of water, one cold, one hot, and one half-way between those two temperatures…

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BA: What you are experiencing is due mainly to the fact that sensors for skin temperature respond much more strongly to changes in skin temperature than they do to a constant skin temperature…

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BA: I bring up this example to illustrate how the relationship between an environmental variable Qi and its perception p may change as a consequence of exposure to conditions. Â

RM: Qi is not necessarily an environmental variable. In most cases by far Qi is a function of environmental variables.Â

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BA: Now imagine that you are trying to control the temperature of your bathwater by dipping your hand into the water while the tub is filling and then adjusting the temperature of the water coming out of the spigot. In the end the water in the tub feels about right and you get into the tub. Initially the water feels satisfyingly hot to you, but after a short while it seems to have cooled considerably and you begin to add more hot water to bring the temperature up. Some of the apparent cooling may be real – the water is gradually losing heat to the environment, after all. However, most of the apparent cooling may actually reflect the fact that your skin temperature has come to equilibrium with the temperature of the water,

RM: No, you have the same reference for a perception that is some function of water temperature.

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BA: and this has caused a reduction in output from the temperature sensors in your skin. You still have the same reference for the temperature you perceive,

RM: Yes!

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BA: but you now perceive the temperature to have fallen a good deal (p is much lower) when in fact the water temperature has hardly changed (Qi is nearly constant).Â

RM: No, what has been found is that the controlled variable, Qi, is not water temperature. Qi is the adapted value of the water temperature. This can be illustrated in a control task where the supposed controlled variable is presented in a variable context, where the context is analogous to the adapting effect of exposure to water temperature. For example, suppose you asked a person to control the size of a circle. But you present the circle in the context of a set of other circles that are made to vary in size, as in the classic illusion shown below.Â

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RM: If you think of the size of the center circle – the one whose size is to be judged – Â as Qi then it will appear that the subject is controlling a perception of Qi that is varying inversely with the size of the context circles. To an observer it would look like the controller is doing a poor job of controlling Qi. But that’s only because you have not correctly identified Qi. When you realize that Qi is actually something like the ratio of the size of the center circle to the size of the context circles, then you will see that Qi is controlled nearly perfectly.Â

RM: This example shows that when a variable is not being controlled well – when what you think is Qi, the controlled variable, is poorly controlled – the explanation (from a PCT perspective) is that you may have identified the wrong controlled variable. In the circle size control example, you assumed that Qi = area of center circle when, in fact, Qi = area of center circle/area of context circles. In the bath tube example, you are assuming that Qi = water temperature when, in fact, Qi = something like water temperature/exposure time.Â

BA: Cases like this demonstrate why it is important to understand that control systems control p directly, and control Qi only indirectly through the linkage between Qi and p.

RM: No, cases like this demonstrate that Qi is not always what you think it is. That’s what the Test for the Controlled Variable (TCV) is for. It’s used to determine what Qi is when you see examples of control behavior. Now that you understand this – that Qi is the CV in TCV – perhaps you will add a chapter or two to your best selling research methods book on how to study living control systems using the TCV. I think that would be a great way to publicize PCT to the experimental behavioral science community.Â

And thanks for the great idea for a new demo!

BestÂ

Rick

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery