[From Bruce Abbott (970524.1415 EST)]
Bill Powers (980523.0323 MDT) --
Bruce Nevin (980522.1323 EDT)
Has the universal error curve been measured in living organisms, or is it
an explanatory construct (a very elegant and simple one!) in models?
It's a phenomenon, as far as I know. Even a dog on a leash shows the
giving-up effect when you drag it away from a delicious smell. I haven't
yet tested any model of it formally in an experiment. The mechanism of the
"universal error curve" could be an actual nonlinearity in a comparator or
output function, or an action of a higher-level system that reduces a
reference signal as a mean of avoiding attempts to produce amounts of
effort that might damage the organism. Or both. It seems to be a fact that
organisms give up when overwhelmed by disturbances -- at least higher
organisms. That's more or less the connotation of "overwhelm." The
universal error curve is just one possible way of modeling this effect.
It's one I would avoid. The universal error curve strikes me as a patch on
the model -- a way to get the model to mimic the observed phenomenon through
an ad hoc addition. More to the point, it is a way to get a one-level
control system to mimic a phenomenon that is more likely a product of
hierarchical control (your second suggestion, which to me seems more an
alternative to the "universal error curve" than another version of it. In
my view, the person who gives up resisting being dragged off to the paddy
wagon hasn't reached a point along the output function where increasing
error is producing decreasing output; rather, a higher-level system has
evaluated the situation and cancelled one course of action in favor of
another. The person being dragged off to be tortured may continue puting up
resistance (to the point of physical exhaustion), and it would be hard to
argue convincingly, I think, that this person's error signal simply hasn't
reached a high enough value to bring it into the declining regime. In that
case, alternative modes of control are not available for consideration and
the danger is imminent, so the only course of action available is to
continue exerting maximum output to oppose the disturbance.
The "universal error curve" is a neat idea ("elegant" as Bruce Nevin put
it), but from my perspective is looks like more like curve fitting than a
realistic solution to the problem.
By the way, your suggestion does have application is real, human-designed
control systems, as you may be aware. An electric furnace whose
thermocouple open-circuits would normally be driven to maximum temperature
(melting the heating elements) as its controller attempted to "see" a
thermocouple voltage corresponding to set point. Naturally this was an
expensive failure. The solution was to design a controller using
essentially the "universal error curve." In this controller, an
open-circuited thermocouple produces a zero error rather than a maximum one.
Regards,
Bruce