[From Bruce Abbott (2017.02.25.1010 EST)]
In my previous post [Bruce Abbott (2017.02.24.1220 EST)] I described how adaptation of sensory receptors to ambient conditions changes the relationship between the environmental controlled variable (Qi) and its perception, p. Adapting the temperature sensors in one hand to cold water and those in the other to hot water gives rise to the surprising perception of two different water temperatures when both hands are plunged into water of an intermediate temperature: The hand previously adapted to cold water now feels warm and the one adapted to hot water now feels hot.
Another example we all have experienced is adaptation to darkness. A change in illumination from bright to dark brings about a gradual increase in the sensitivity of the photoreceptors in the retina. Consequently the threshold intensity for perceiving the light decreases over time following a transition from light to darkness. These changes can be observed experimentally by giving a participant control over the intensity of a light-source. The participant is asked to adjust its intensity until the light is just barely perceptible. In this way the threshold is sampled after various intervals of time spent in darkness. Such experiments demonstrate that the sensitivity of the rods (the photoreceptors that give us night vision) increases up to a million-fold after a change from bright light to complete darkness.
To my mind, the logical way to represent such changes in a control-system diagram is as a change in the input function that converts Qi to p. To conversion formula would compute p from Qi as a dynamic function of time and the recent variations in light intensity to which the eye was being exposed. In this system, Qi remains the intensity of the light – out there in the physical environment – and p is the perception of the light’s intensity.
Rick Marken (2017.02.24.2100 PST) offers an alternative proposal. According to Rick, light sensitivity changes should be viewed as producing a change in Qi. In Rick’s view, Qi is not the physical intensity of light but the physical equivalent of p, obtained by solving the input formula for Qi and plugging in the value of p to obtain the equivalent Qi. According to Rick, Qi is not the intensity of the light, but the adapted intensity of the light.
What Rick’s solution does is to make Qi the combination of environmental variables that is equivalent to the perception. The combinatory rule is not present in the environment, however, but in the system’s input function. This makes Qi equivalent to what the observer would infer is being controlled by the system.
I think it makes more sense to think of Qi as representing one or more physical variables out there in the environment (like light intensity), where they can be observed and measured, and letting the system’s input function determine how these variables get transformed into a perceptual-signal representation. That way, what changes during sensory adaptation is one’s perception, and nothing changes in the environment. Adaptation occurs in the sensitivity of the receptors as computed in the input function – in the gain – and this changes how p relates to these input quantities.
However one prefers to describe and label the input variables and Qi, the same mathematical transformations occur around the loop and the system behaves in exactly the same way. When discussing how sensory adaptation affects the perception of input variables such as skin temperature or light intensity, I think it makes for a clearer discussion to treat Qi as the environmental variable, p as its perception as determined by the input function, and adaptation as involving dynamic changes in the input function. That way it is one’s perception of the environmental input that changes during adaptation, not Qi.
Bruce